diff --git a/Notebooks/HughHubbarrdDimer.nb b/Notebooks/HughHubbarrdDimer.nb index a677470..4331518 100644 --- a/Notebooks/HughHubbarrdDimer.nb +++ b/Notebooks/HughHubbarrdDimer.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 6738264, 120753] -NotebookOptionsPosition[ 6722687, 120496] -NotebookOutlinePosition[ 6723023, 120511] -CellTagsIndexPosition[ 6722980, 120508] +NotebookDataLength[ 6797090, 122171] +NotebookOptionsPosition[ 6778790, 121872] +NotebookOutlinePosition[ 6779127, 121887] +CellTagsIndexPosition[ 6779084, 121884] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -120491,11 +120491,1387 @@ Cell[BoxData[ Cell[BoxData["0"], "Output", CellChangeTimes->{{3.814730565781144*^9, 3.814730586270438*^9}}, CellLabel->"Out[18]=",ExpressionUUID->"af287abc-d325-4b3d-b738-17f8150381b7"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[""], "Input", + CellChangeTimes->{{3.815385799505107*^9, 3.8153858234716578`*^9}, { + 3.815385891799666*^9, 3.815385892679685*^9}, 3.8153878465813227`*^9, + 3.815392269739161*^9},ExpressionUUID->"78e9de6a-84d5-4c17-ad21-\ +26acac8ce5b9"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"-", + FractionBox["2", "7"]}], ",", + RowBox[{"-", + FractionBox["2", "343"]}], ",", + RowBox[{"-", + FractionBox["90", "16807"]}], ",", + RowBox[{"-", + FractionBox["4408", "823543"]}], ",", + RowBox[{"-", + FractionBox["215100", "40353607"]}], ",", + RowBox[{"-", + FractionBox["10493194", "1977326743"]}], ",", + RowBox[{"-", + FractionBox["511671690", "96889010407"]}], ",", + RowBox[{"-", + FractionBox["24939787310", "4747561509943"]}], ",", + RowBox[{"-", + FractionBox["1215097665750", "232630513987207"]}], ",", + RowBox[{"-", + FractionBox["59176067699278", "11398895185373143"]}], ",", + RowBox[{"-", + FractionBox["2880691830972990", "558545864083284007"]}], ",", + RowBox[{"-", + FractionBox["140172399363367356", "27368747340080916343"]}], ",", + RowBox[{"-", + FractionBox["6817770255624312240", "1341068619663964900807"]}], ",", + RowBox[{"-", + FractionBox["331463277996975211494", "65712362363534280139543"]}], ",", + RowBox[{"-", + FractionBox["16107963986540966246550", "3219905755813179726837607"]}], + ",", + RowBox[{"-", + FractionBox["782450595553162414323912", "157775382034845806615042743"]}], + ",", + RowBox[{"-", + FractionBox["37991201666918677187968620", + "7730993719707444524137094407"]}], ",", + RowBox[{"-", + FractionBox["263402330169755850506935210", + "54116956037952111668959660849"]}], ",", + RowBox[{"-", + FractionBox["89445682036655609650321589550", + "18562115921017574302453163671207"]}], ",", + RowBox[{"-", + FractionBox["4337172533719326445821751789976", + "909543680129861140820205019889143"]}], ",", + RowBox[{"-", + FractionBox["210212234902629743740498515682980", + "44567640326363195900190045974568007"]}], ",", + RowBox[{"-", + FractionBox["10183838948115639122284418890474222", + "2183814375991796599109312252753832343"]}], ",", + RowBox[{"-", + FractionBox["493134576562428402367573008957553230", + "107006904423598033356356300384937784807"]}], ",", + RowBox[{"-", + FractionBox["23868098599153305286239494266170655438", + "5243338316756303634461458718861951455543"]}], ",", + RowBox[{"-", + FractionBox["1154693026066092132492247882693897284750", + "256923577521058878088611477224235621321607"]}], ",", + RowBox[{"-", + FractionBox["55835369989313759014432001510312806419314", + "12589255298531885026341962383987545444758743"]}], ",", + RowBox[{"-", + FractionBox["2698634322425987406700770083534724848607090", + "616873509628062366290756156815389726793178407"]}], ",", + RowBox[{"-", + FractionBox["18623870162377614856241535500851758344011660", + "4318114567396436564035293097707728087552248849"]}], ",", + RowBox[{"-", + FractionBox["6294751145088872267964279399685388382602203200", + "1481113296616977741464105532513750734030421355207"]}], ",", + RowBox[{"-", + FractionBox["303789678759638343704247326622933671662553085930", + "72574551534231909331741171093173785967490646405143"]}], ",", + RowBox[{"-", + FractionBox["14653735999608130678975266559142871665922018020250", + "3556153025177363557255317383565515512407041673852007"]}], ",", + RowBox[{"-", + FractionBox["100926087646316177921131480378270627335845292983730", + "24893071176241544900787221684958608586849291716964049"]}], ",", + RowBox[{"-", + FractionBox["34043095710661802458884608123535583749367184776770150", + "8538323413450849900970017037940802745289307058918668807"]}], ",", + RowBox[{"-", + FractionBox["1639560919216914125112900008067949137395060726280045390", + "418377847259091645147530834859099334519176045887014771543"]}], ",", + RowBox[{"-", + FractionBox["78921131483084942257541590236229900153725535603142826750", + "20500514515695490612229010908095867391439626248463723805607"]}], ",", + RowBox[{"-", + FractionBox["3796840500928359912550075350316301701199094591161692860120", + "1004525211269079039999221534496697502180541686174722466474743"]}], ",", + + RowBox[{"-", + FractionBox[ + "182562070147546947458636043024920845770407906434848990365700", + "49221735352184872959961855190338177606846542622561400857262407"]}], ",", + RowBox[{"-", + FractionBox[ + "8773108408989221512878955015994724699337981750276546405374750", + "2411865032257058775038130904326570702735480588505508642005857943"]}], + ",", + RowBox[{"-", + FractionBox[ + "421353420840363630671542778440347337936299796364909799224742750", + "118181386580595879976868414312001964434038548836769923458287039207"]}], + ",", + RowBox[{"-", + FractionBox[ + "20224821481054144396928282530599010309253873809639646884097393370", + "5790887942449198118866552301288096257267888893001726249456064921143"]}], + ",", + RowBox[{"-", + FractionBox[ + "970203368276049305975472772632402903065137634190543126968763332850", + "283753509180010707824461062763116716606126555757084586223347181136007"]}\ +], ",", + RowBox[{"-", + FractionBox[ + "46513092374796497845319528519835123834593845364693063739857699535690", + "13903921949820524683398592075392719113700201232097144724944011875664343"\ +]}], ",", + RowBox[{"-", + FractionBox[ + "318359688617842571126655768689631645351086220983427039134602832558550", + "97327453648743672783790144527749033795901408624680013074608083129650401"\ +]}], ",", + RowBox[{"-", + FractionBox[ + "106703633993890250512301762653784002074148135731323331320012135382378660\ +", "33383316601519079764840019573017918591994183158265244484590572513470087543\ +"]}], ",", + RowBox[{"-", + FractionBox[ + "729390024209173085086966615497505771616034966250242715149145694421708000\ +", "23368321621063355835388013701112543014395928210785671139213400759429061280\ +1"]}], ",", + RowBox[{"-", + FractionBox[ + "244143396410705632202107021236765526405933995569726864725312762621784481\ +330", "80153343160247310515380886994816022539378033762994852007501964604841680\ +190743"]}], ",", + RowBox[{"-", + FractionBox[ + "116662974600902294068280888675691208511920713644965400414559108182937235\ +54050", "392751381485211821525366346274598510442952365438674774836759626563724\ +2329346407"]}], ",", + RowBox[{"-", + FractionBox[ + "557075453544791273194099958825642058881720062103828680425687367990548509\ +555100", "19244817692775379254742950967455327011704665906495063967001221701622\ +4874137973943"]}], ",", + RowBox[{"-", + FractionBox[ + "265814917161629464510898687286516624227932761414967361182498467974624660\ +05458000", + "942996066945993583482404597405311023573528629418258134383059863379501883\ +2760723207"]}], ",", + RowBox[{"-", + FractionBox[ + "126741802871864205760510314300457789794039365425482068957712288120226923\ +3057197898", + "462068072803536855906378252728602401551029028414946485847699333055955922\ +805275437143"]}]}], "}"}]], "Output", + CellChangeTimes->{3.815385826782214*^9, 3.815385893844574*^9, + 3.815387847378438*^9}, + CellLabel->"Out[24]=",ExpressionUUID->"3018b4f4-0608-4636-83fb-d2661d7ae819"] +}, Open ]], + +Cell[BoxData[ + RowBox[{"Ans", "=", + RowBox[{ + FractionBox[ + RowBox[{"Root", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"4", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "4"], " ", "\[Lambda]"}], "-", + RowBox[{"4", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "4"], " ", + SuperscriptBox["\[Lambda]", "2"]}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"2", " ", + SuperscriptBox["U", "4"]}], "-", + RowBox[{"8", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "2"], " ", "\[Lambda]"}], "-", + RowBox[{"2", " ", + SuperscriptBox["U", "4"], " ", "\[Lambda]"}], "+", + RowBox[{"4", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "2"], " ", + SuperscriptBox["\[Lambda]", "2"]}]}], ")"}], " ", "#1"}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"-", "3"}], " ", + SuperscriptBox["U", "2"]}], "+", + RowBox[{"2", " ", + SuperscriptBox["U", "2"], " ", "\[Lambda]"}]}], ")"}], " ", + SuperscriptBox["#1", "2"]}], "+", + SuperscriptBox["#1", "3"]}], "&"}], ",", "1"}], "]"}], "U"], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"U", "\[Rule]", "7"}], ",", + RowBox[{"t", "\[Rule]", "1"}], ",", + RowBox[{"\[Lambda]", "\[Rule]", "1"}]}], "}"}]}]}]], "Input", + CellChangeTimes->{{3.8153919172069397`*^9, 3.8153919281313667`*^9}}, + CellLabel->"In[58]:=",ExpressionUUID->"405dd260-566e-4a6b-963f-b2d59b93de2d"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + FractionBox["1", "14"], " ", + RowBox[{"(", + RowBox[{"49", "-", + RowBox[{"7", " ", + SqrtBox["65"]}]}], ")"}], "*", "1."}]], "Input", + CellChangeTimes->{{3.815392702206225*^9, 3.815392703981442*^9}}, + CellLabel-> + "In[152]:=",ExpressionUUID->"72cdc13b-54ff-4fa8-b2ed-ba6038d95215"], + +Cell[BoxData[ + RowBox[{"-", "0.5311288741492746`"}]], "Output", + CellChangeTimes->{3.815392704348737*^9}, + CellLabel-> + "Out[152]=",ExpressionUUID->"5de04214-f291-4d6b-ac80-77c6ac510684"] +}, Open ]], + +Cell[BoxData[""], "Input", + CellChangeTimes->{{3.815392151009489*^9, 3.8153921730909157`*^9}, { + 3.815392280447318*^9, 3.815392308850752*^9}, + 3.8153936406432867`*^9},ExpressionUUID->"28cd698a-a821-40fa-bd88-\ +be3b282bfc34"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ListLogLinearPlot", "[", + RowBox[{ + RowBox[{"{", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"x", "-", "1"}], ",", + RowBox[{ + RowBox[{"Sum", "[", + RowBox[{ + RowBox[{ + "UMPseries", "\[LeftDoubleBracket]", "i", + "\[RightDoubleBracket]"}], ",", + RowBox[{"{", + RowBox[{"i", ",", "1", ",", "x"}], "}"}]}], "]"}], "-", + "Ans"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"x", ",", "1", ",", "100"}], "}"}]}], "]"}], ",", + "\[IndentingNewLine]", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"x", "-", "1"}], ",", + RowBox[{ + RowBox[{ + "Richardson1", "\[LeftDoubleBracket]", "x", + "\[RightDoubleBracket]"}], "-", "Ans"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"x", ",", "1", ",", "98"}], "}"}]}], "]"}], ",", + "\[IndentingNewLine]", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"x", "-", "1"}], ",", + RowBox[{ + RowBox[{ + "Richardson2", "\[LeftDoubleBracket]", "x", + "\[RightDoubleBracket]"}], "-", "Ans"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"x", ",", "1", ",", "98"}], "}"}]}], "]"}]}], "}"}], ",", + "\[IndentingNewLine]", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", + RowBox[{"Red", ",", "Green", ",", "Blue"}], "}"}]}], ",", + "\[IndentingNewLine]", + RowBox[{"Joined", "\[Rule]", "True"}]}], "]"}]], "Input", + CellChangeTimes->{{3.8153858302277308`*^9, 3.815385863686636*^9}, { + 3.815385896302168*^9, 3.8153859211818333`*^9}, {3.815387700636529*^9, + 3.815387706096195*^9}, {3.8153877443392057`*^9, 3.8153878254596643`*^9}, { + 3.8153916097478313`*^9, 3.815391613832102*^9}, {3.815391678123755*^9, + 3.815391680631074*^9}, {3.8153918342086763`*^9, 3.815391886099485*^9}, { + 3.8153919315581408`*^9, 3.815392087065661*^9}, {3.8153922212271*^9, + 3.815392235407214*^9}, {3.8153923553363943`*^9, 3.815392357381094*^9}, { + 3.815392435311534*^9, 3.81539243971887*^9}}, + CellLabel-> + "In[124]:=",ExpressionUUID->"3b3964cc-070a-4db7-9913-448b56d90c7b"], + +Cell[BoxData[ + GraphicsBox[{{}, {{{}, {}, + {RGBColor[1, 0, 0], PointSize[0.007333333333333334], AbsoluteThickness[ + 1.6], LineBox[CompressedData[" +1:eJw1VHlQ0/cSD5oYSEjy+0VFgVKqlpFLGA9QyrELKgVU8EAFDIrYKAI+UYIc +3iheCA2J1UqlgKFAORWqHIF8OeRSoQIWW/GNVpABYwtMeBiQ4/Hm0Z3Z2T8+ +szufz15Lgo9uF89hMBgHZvx/8R97R/3UpDr8Kww6jE+52fRBuItRWmFeG3Dn +Fsa9lw/DItOBPXafWmfxUYh01MS2b2qF1Ul/fXStGYM0vjNredpTmPOF5Tg3 +fwKErEcP3AafwO6AVUXHl05DabfPQXu3JxCZ7wgldxko0ZQlzr/5eLa+Dvpm +iILU71vAYOcD5f2wOdjL93zdhi2wee3Zsh6buchs7q9pu9UMp3/srDL4cy7q +RzZGfxpsgm3XV1oxE5iYpdq3QuzZBDnKFwaPP2PhATWfGGc1gqnHFgeDPBb6 +lHCUNozGWf7zUN/hdGBhYAPEnR2vDcubhyxVSVJ21SO4lBL21UlTNu5LD+o2 +N3kE1qXMefbJbOzazTrldrYeUnoiT7p9ZGMJM9hDp6cO7hcdvWGzRxdNGfzK +4x510NzgHC2p1EX9+WYDiuJaGCptnzy9UA9PVFDXMhfXwpi17FROuB5WqMPV +0RdqZvunh1ZFdL/4DYFWo6H3NygO2rax3aqqVSC9OLf8dSAH3w7zdfXSq2GZ +182ugFwOJgkdL+y/WAWmU61P1g1xUOLhafryiBJ+6OKOZdtxMbaw7tClPZUQ +YJXi0RbDRZ3iAFbslgoIay5XdVZwcaXlVWX9+nJoL/9t5HctFxffCToY7VIG +o7yK8xN2+tiYlqFVOD+EBo1gR8AxfRzoYMb5uT6Yna8+avY9Yyk8f4Hqpq/+ +Nu/Rxyvq71qku0oh17W+odGQh7dMnJg2ISXQxbsSMubNwz2nXViXztwH3vFV +jp3xPJScsbRW3L4H3gXJG8UPePhMe++ZSWQxrHC28SV9PFyXXXNMUVUI9IcF +BkMGfPzlG5l/n6AA1vtO2LPc+egi6W/UhOdBVoviBFfCx/LKeKMXnbkQ7iat +5mfyUTvc/fvtDTnwcEhqa9TKx75xv4L15CeIUm51Wqflo1TTf+jl+qzZ/RQg +ShdwgjvuQrFxQVnHJgEaGp2seRWaCdOMbdNBEgF6+CvVXrwM8Py5KM/sjgB3 +WCR9vSsyDfKdloaY1wtQFLY2duR1KujPr4uOGBDgLr32mweDvgfNVKV/PJtC +x3smfukj38HWcMsn/zGk8MOMqOQ7cvBPLcxcaE1hX31M8ed+KbDFvbGh15nC +pG7B00jvZIi1aBoT+1CoiTFyuDb/GiSuEr/6IYhCxXOG8cbpBOCFC9VXjlHI +uVmZFUzHg/rV8ou28RSmT51os5OfAuPFPf0pMgpDzTa9A5+o2fub4RNX9ja6 +IByiLG7IZSUUmpfi+e60vZC9zOvlmjoKfazu2C1ftgZW0ObDqe0zfBSJvx0+ +vIM4tCkzGt9QGFVea8TeKyZKoxtpFYMULhQfeJrtFEGWuB66GjVFYcEObxPr +i1GkpevLkU/6NBp++JqbcCmOwO4RkbcxjX9Muhwp2HCW9NkuXf0vCxqzBj6y +O1+fJyb5E12itTRGHHe1hYkLRMS+m2q8kcYM+yGmmTaBCPtr6vK30/iMDn0h +fH6ZOK3afJkfRKOPa3J1qvQqsfBetmDjERq3X68J2W6TSCLvF1/dGkfj1rKE +0Y7C62TDuZjJlZdpHOWS2nJBMvn//6ExXCVbrfD9lojTsueczKCxLJbtleoi +JfG9wUm9BTT+KvX6S7dBSp6LR/XMK2iMrebBsHMK4Si0e90baJw3mbs09+cU +4l49EIrtNFZtFiVe0JWRDpAxF/2bxnEq4JuXATISdCzw0+N+Gr8/+iKGmSkj +o9eKFgWO0PjnGgtRQLeMUNYrjdumaWQ0a7bZceREJTKr/ZwrxIR0if3gCjmR +hOSofAyEeEuqPvjWXU4iujR1+5cI8VtHy7zDO+XkNsmJ3mktRAfiY/jGX056 +qibPWa0VorLmoW6mr5xos9hnel2F6FphPMyeyddueqd7frMQbUQ6/hE2chIq +0T7U2S3ElGY/lR1fTqxMDAwP7Z/BF0WeK30nI/8FtibKKg== + "]]}, + {RGBColor[0, 1, 0], PointSize[0.007333333333333334], AbsoluteThickness[ + 1.6], LineBox[CompressedData[" +1:eJw1lHs0lAkUwD2bGDO+byphbDZKSIoeegzfVdhKScWSaKUmU1JiCsnGbC8p +GU0PoSgh463BzMQVUYn2CJM67ZaEogexImLtqb3n3HP/+J1z3/fO9Nu/iaui +pKS0fUL/s/9Lf8C54OSeBurTsq9jKy07qcBXJ545JNdTdNXcw93n+6jj8WTz +TdtHP/gg5bh1p3Xk64fUwrMfvthXDlO/tewybYh5QKn8bP6VLh6lwtovxrxf +eJ/y8LLOCzYap8oT44WGbTVUiHgFVXRdCTbRBOrZwns//CtDX99l98eO1ZSO +u0ReGKACoGoibPh2l1pnc7S03VIVuPXrNndJK6nIq013dNpUIen8jO3FAxXU +xjNWc9WOq4GJ39s1Vb/foTLlT3XqDNQhyOSa+gGWjDJcvX6ZTrY6rOLsumdV +UPoj/0mgx9YxCvGUUIePfr0bkD0JpBbPaKn0YuqEMGB5hCENeKmLzhnWFVAW +xWqTlsTRYHQHveGWaS4lbA+JWPmFBtcSBgPtWrKowrz9Isutk8FAYKJbfCWd +elBjG8qXTQaOvkO4JDyV6i1u/BY5TQPiIsXuLR2XqWGLhCOZezVgmZ3NtL8Z +wh/904Au/klPz2cCqkG/t1tEaII5sBLT9X2p+GOqZS99NKFd8rTv0m0+Gq+9 +qPDK0gROglN4xi+n0HCs4dHSXk1QPtYf0/IyAZMU9OGMxXTYdsaN7uebiF5z +hasfh9GhSuzRVJl+DQMelFU0Selg5OIXaaK4jo1lLQOtQ3SIdbfzWi6/iYMM +afToYi3o5njmekdnYU2/9mavA1qwK79E5mEqxu/z1QK1Lgef8fxcLL+//KNp +uxbYZFRE62oVYJZ9dU2tHgNinf2bdy8oRAXjFG/YhQFFv7Z19DgUISPYekWT +gAERLaEFSWuK0SUnzpErYYDu2m1th+1u4zxbSzfsZIBgnsqf54wlSL6fqtOr +w4RHoY2BHUMSXOU2ukTdiQmzREdWxVaUYPrDG4fofCY0i2WeF/iluHdlfDkz +jQlLJJfMDNhlWNIbP1+/gQkXrd1EnKIyPCh35SwdYsJu2sva6cul+H0/teGG +/WfzpiIp5rNzSp84a8PDOS9cLxvIcFxp47gvXxsinMdaRaEyXHMrL3t2sjaU +1Wl5f62WoZhjxDOt1oZQV91NY8py1JpSFRr0Thue1gYOPbOSY/+YbIuARoCz +pseSus1ydN1r/ugfPQI2Oj6I0ubJccuV3LRpFgS0flIv/7BPjuudamve2BIg +lW8wypng4Wb3h7kbCLBVTtG/4C7HWGvuiyTfCS4INRpcLEfGXlbPqQME7EpR +zjLUlGPPiznH5gsI8LBZ/G7nExmyddvfChMIeP6R18g+J8Pv90dAtJ2ZIhlk +eNBMdD6hiIC64JCmlV1SzDBe+3xRFQF+wb5de/6Q4jzStO9KIwF3w9av50+T +4rLH8tTaVwR8HolfWplShnJ9UYr0EwGzNevyCg3KcKa9f8zBMQLSwlu35yaU +4kPFrIERLRKuu5yJ0VMqRcpjwNuFTcLNcv1yH24Jds43WrjPjITzlv71r6sk ++JN4VOFtQ0JcimUiS0+C3rTrV9iOJBjfMu714N1G1tvKKvEmErxiNfxmFBYj +x3rdSaYvCaeNXxg86S9CMxfjqY6BJOjqT6l5uaAIQwrzY1wPk+Cvztxwm1eI +DlFh36xOksB1LW29k1SA3/8PCZs/KiY1iPKRm5KhEpFKgunIjmROdy4K3vid +fZNDwo7k7FdpS3OwmTuoYSqdiNdTz2uJykbNG0PbnGpIYL8OzsyrzkKn8nd7 +oJGEtrH6dFWVTHxCJahN/2uiXmdpaRbnJvoe8Bmpe0vCuMAIgvg3cPB03nSf +ARI6DxX4mWenIWFhxX48TsL+nZWxa8qvYYX37Lsz6CwYsV+Y5jY7Gfm8zIoN +Oiw4nZPfrB53GYMU/VXbZ7KAFPWGdw6JMBEzQ90tWHDSJaY3zF+I7Xe+Rc21 +YUF/xxyfoJJYHEqn/f7GngVK3ZyrluJjOOTcMTl6HQv6/NuFar4R+C9U9t+P + + "]]}, + {RGBColor[0, 0, 1], PointSize[0.007333333333333334], AbsoluteThickness[ + 1.6], LineBox[CompressedData[" +1:eJw1VHs01HkUnzyHMeP3Gxlb0ks2Iootj7TfOyqlopSyTfQ6pmVJhJTWKj08 +eqxnVlHe8s4jjDHznUfKI3alnbaHyhlEdhcljDC7e2rvOffcPz7n3PM5n8/n +3iVHju/iqlAolMP/9n/z/yq+oUJPH2tDw/ZTs06W/egWZHRovG5BNNWyiHfJ +o8jn8hskevbwCz6Oklv85x77ownZXP1rgi1SoDqNn6cduqVIZfGKKVrJNLra +GFlUPyBGnhzr8hNLlaiOfmut0QRGISXrUFUOBZ7bDZpji8Yv++eASw7bISWk +HrH23ONX+quAXaiR42+PatB226g6uaUqGEwojmTaV6LIW12NrB5V6DrhHGl7 +sgS5X1ltrnZRDXI3XkoW5+WhQv5TVusCdTD0ODj8Yk4GWrTF1Z5VrA5y5qD6 +kPW1L/w1oNnWVtif5YMioqbE/sUasN2JSDLWP48vJfo7nFmkCePC6IUWKBVb +VKtprL2mCXutd6Sv35CFE+UhZ5wmNIFiPMUWlufjyvLjKZb7qXDSVP1y5Zti +3Ny0Pjy0gQqOVgM2j55W4JHqzplIfS24dJTicdylCisskn4sDNCCmoyWih9i +a/Bn/bQg7QNO97pTi9vnj7xLIbTBzuxR59M79Tjhgmr9a29tSH0rjomMa8DG +W6/LOHe0wahCP3jGpREvmm1vsxvRBt+eJ0/13wnwTRlNUbCGBgVZPTnJfhhz +zBO3dJyiwfl8vrmZjwj7N9cLu3g00KhWai1UFePO+t/H/pikQf7gYkleohiP +03nnptfowFFm1FuRrgQ3fdDdzQnWAdaxqG8jIyX4s7868KNhd+nQcwkWPHT4 +21SuA9TbbV+bmErxHba06cE8OrjqT/7iwpViGT3WV+FGh75vw3+NSpJi+gnr +dV3RdLCortj3sUKK3UqvbeLeo4N0dKf/K4EUr1xv6YH76fBms19DWKMUk3/O +ZY2wGCBrKONMl0jxBo/pterODDjJoV7nXZHivJbck7RQBlhdiJZMHZDiAKcE +ASObAfr8bH09YymuHUmwmt/OgKPNbmH7n0lwGH+no90kA2JeHHS2jpbgz/nU +BQfP13afjCS4wrC07vE2XRiVmzEXlYmxkuKuPBSqC4XrlKG0VWLsUlRebJKh +C33vswutC0W4xHGpr6lUF/o3GH9H0xNhHT1JeNCgLpxdPipYPCDEH2Yb9kVr +EhC34L3ybKoA7wxY0fZxHgHx1+/vdrRqxPtulGXrWxDA/lvD70BtA3Z1ftDU +u54A6PFepzDn4dNmDxXcHQTEBJrEL0usw5etuS9vHiIgXbDKbab/HqYHMIdi +gwlIY7xYmW9Zg4deLr9gFU0Ab3npMNuvCht+JR9ITCIgg9Y1NJ12F3++PwKe +TIQo1E6V4TCzlOSkKgI4rX91q5QV4QLjrc+/kRDQmlrb49GZj1eSpqM3OgkY +dW1XPfg2G9t38LMevCFgb3V4HF1+E/Pnp2TyhglwVZrRfXqT8RL293FhswTY +B+rxDCpicIts2dgnHRJy3X38vbQDMfIc83IzJIGjvNYedDQY9VsttQk0I2F/ +JJHbNxCLjEqmZV62JLgXPVDExacgL82cG4abSNjsvJyP0jIQc0AkKdlFQka8 +ZAdlWw5ytN4ewzhEwupc9+5l7AJk5mY8d9MxEt47BXn+bl6MQior4nZGkDDl +sLtLTi1HG8+emlkdQ8K8iMDfWEN3v/wfEjKFXKOO5irEzSxQOZNFQmKzylfJ +GTUouvfI1d5SEjpud6r4cmvRE+64limPBOqeoti9S+uRdu7kAecmEqwyX5kE +PeYhZ8HgD9BJQtHbrVc7QvnoMUpSM+gmoXTrLDWFKkCHgr0/tQ6QkN8RKhu6 +IkTj8eUG3mMkXB6eiy5SRIiwWG3YoSQh/rSNnkGVCAm9TMQLaUw4HHA96FeO +GIX6Fgp3sJjg0HAlwnNKjIJkHySHlzDhyPy0BO8ECUrHheF7LJgQ9an8WOoC +KZI3zpw1t2XCvva+jfW3pGgyT/OnXjYTZJd2vbjAuo8mt/VRz21ngkfqxtv4 +/H30DwRn3sw= + "]]}}, { + {RGBColor[1, 0, 0], PointSize[0.007333333333333334], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 1, 0], PointSize[0.007333333333333334], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 0, 1], PointSize[0.007333333333333334], AbsoluteThickness[ + 1.6]}}, { + {RGBColor[1, 0, 0], PointSize[0.007333333333333334], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 1, 0], PointSize[0.007333333333333334], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 0, 1], PointSize[0.007333333333333334], AbsoluteThickness[ + 1.6]}, {}, {}, {}, {}, {}, {}, {}}, { + {RGBColor[1, 0, 0], PointSize[0.007333333333333334], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 1, 0], PointSize[0.007333333333333334], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 0, 1], PointSize[0.007333333333333334], AbsoluteThickness[ + 1.6]}, {}, {}, {}, {}, {}, {}, {}}}, {{}, {}}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{-0.19345773674611771`, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, { + Charting`ScaledTicks[{Log, Exp}], + Charting`ScaledFrameTicks[{Log, Exp}]}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImageSize->{896., Automatic}, + Method->{ + "OptimizePlotMarkers" -> True, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Exp[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Exp[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{-0.19345773674611771`, 4.59511985013459}, {-0.1542318367009, + 0.24541458843498912`}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.05], + Scaled[0.05]}}, + Ticks->FrontEndValueCache[{ + Charting`ScaledTicks[{Log, Exp}], Automatic}, {{{0., + FormBox["1", TraditionalForm], {0.01, 0.}, { + AbsoluteThickness[0.1]}}, {1.6094379124341003`, + FormBox["5", TraditionalForm], {0.01, 0.}, { + AbsoluteThickness[0.1]}}, {2.302585092994046, + FormBox["10", TraditionalForm], {0.01, 0.}, { + AbsoluteThickness[0.1]}}, {3.912023005428146, + FormBox["50", TraditionalForm], {0.01, 0.}, { + AbsoluteThickness[0.1]}}, {4.605170185988092, + FormBox["100", TraditionalForm], {0.01, 0.}, { + AbsoluteThickness[0.1]}}, {-0.6931471805599453, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {-0.5108256237659907, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {-0.35667494393873245`, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {-0.2231435513142097, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {-0.10536051565782628`, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {0.6931471805599453, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {1.0986122886681098`, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {1.3862943611198906`, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {1.791759469228055, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {1.9459101490553132`, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {2.0794415416798357`, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {2.1972245773362196`, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {2.995732273553991, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {3.4011973816621555`, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {3.6888794541139363`, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {4.0943445622221, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {4.248495242049359, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {4.382026634673881, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {4.499809670330265, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {5.298317366548036, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {5.703782474656201, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {5.991464547107982, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}, {6.214608098422191, + FormBox[ + TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}, { + AbsoluteThickness[0.1]}}}, Automatic}]]], "Output", + CellChangeTimes->{ + 3.8153858422843447`*^9, {3.81538589727214*^9, 3.815385921531478*^9}, + 3.815387706909099*^9, {3.815387747876185*^9, 3.815387826236517*^9}, + 3.815387862744269*^9, 3.81539161493594*^9, {3.815391681582279*^9, + 3.815391694474931*^9}, 3.815391762488186*^9, {3.815391850958309*^9, + 3.8153918902846203`*^9}, 3.815391938367367*^9, {3.815391972557735*^9, + 3.815392087456875*^9}, {3.815392214831964*^9, 3.815392235979046*^9}, + 3.8153923188163424`*^9, {3.8153923502816133`*^9, 3.815392358035468*^9}, { + 3.8153924372686787`*^9, 3.815392439944557*^9}}, + CellLabel-> + "Out[124]=",ExpressionUUID->"d258cd3c-d761-4d87-9459-be86bc955d92"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[{ + RowBox[{ + RowBox[{"UMPseries", "=", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"SeriesCoefficient", "[", + RowBox[{ + RowBox[{ + FractionBox[ + RowBox[{"Root", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"4", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "4"], " ", "\[Lambda]"}], "-", + RowBox[{"4", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "4"], " ", + SuperscriptBox["\[Lambda]", "2"]}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"2", " ", + SuperscriptBox["U", "4"]}], "-", + RowBox[{"8", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "2"], " ", "\[Lambda]"}], "-", + RowBox[{"2", " ", + SuperscriptBox["U", "4"], " ", "\[Lambda]"}], "+", + RowBox[{"4", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "2"], " ", + SuperscriptBox["\[Lambda]", "2"]}]}], ")"}], " ", "#1"}], + "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"-", "3"}], " ", + SuperscriptBox["U", "2"]}], "+", + RowBox[{"2", " ", + SuperscriptBox["U", "2"], " ", "\[Lambda]"}]}], ")"}], " ", + SuperscriptBox["#1", "2"]}], "+", + SuperscriptBox["#1", "3"]}], "&"}], ",", "1"}], "]"}], "U"], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"U", "\[Rule]", "3"}], ",", + RowBox[{"t", "\[Rule]", "1"}]}], "}"}]}], ",", + RowBox[{"{", + RowBox[{"\[Lambda]", ",", "0", ",", "i"}], "}"}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"i", ",", "0", ",", "100"}], "}"}]}], "]"}]}], + ";"}], "\[IndentingNewLine]", + RowBox[{"Eexact", "=", + RowBox[{ + FractionBox[ + RowBox[{"Root", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"4", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "4"], " ", "\[Lambda]"}], "-", + RowBox[{"4", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "4"], " ", + SuperscriptBox["\[Lambda]", "2"]}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"2", " ", + SuperscriptBox["U", "4"]}], "-", + RowBox[{"8", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "2"], " ", "\[Lambda]"}], "-", + RowBox[{"2", " ", + SuperscriptBox["U", "4"], " ", "\[Lambda]"}], "+", + RowBox[{"4", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "2"], " ", + SuperscriptBox["\[Lambda]", "2"]}]}], ")"}], " ", "#1"}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"-", "3"}], " ", + SuperscriptBox["U", "2"]}], "+", + RowBox[{"2", " ", + SuperscriptBox["U", "2"], " ", "\[Lambda]"}]}], ")"}], " ", + SuperscriptBox["#1", "2"]}], "+", + SuperscriptBox["#1", "3"]}], "&"}], ",", "1"}], "]"}], "U"], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"U", "\[Rule]", "3"}], ",", + RowBox[{"t", "\[Rule]", "1"}], ",", + RowBox[{"\[Lambda]", "\[Rule]", "1"}]}], + "}"}]}]}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"CumUMP", "=", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"Sum", "[", + RowBox[{ + RowBox[{ + "UMPseries", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], + ",", + RowBox[{"{", + RowBox[{"i", ",", "1", ",", "x"}], "}"}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"x", ",", "1", ",", "100"}], "}"}]}], "]"}]}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Richardson1", "=", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"n", "+", "1"}], ")"}], + RowBox[{"CumUMP", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}]}], "-", + RowBox[{"n", " ", + RowBox[{ + "CumUMP", "\[LeftDoubleBracket]", "n", "\[RightDoubleBracket]"}]}]}], + ",", + RowBox[{"{", + RowBox[{"n", ",", "1", ",", "98"}], "}"}]}], "]"}]}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Richardson2", "=", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{ + FractionBox["1", "2"], + RowBox[{"(", + RowBox[{ + RowBox[{ + SuperscriptBox[ + RowBox[{"(", + RowBox[{"n", "+", "2"}], ")"}], "2"], + RowBox[{"CumUMP", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "2"}], "\[RightDoubleBracket]"}]}], "-", + RowBox[{"2", + SuperscriptBox[ + RowBox[{"(", + RowBox[{"n", "+", "1"}], ")"}], "2"], " ", + RowBox[{"CumUMP", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}]}], "+", + RowBox[{ + SuperscriptBox["n", "2"], + RowBox[{ + "CumUMP", "\[LeftDoubleBracket]", "n", "\[RightDoubleBracket]"}]}]}], + ")"}]}], ",", + RowBox[{"{", + RowBox[{"n", ",", "1", ",", "97"}], "}"}]}], "]"}]}], ";"}]}], "Input", + CellChangeTimes->{{3.815391566946772*^9, 3.81539169148372*^9}, { + 3.815391734713945*^9, 3.8153917525627747`*^9}, {3.815392189116294*^9, + 3.815392207871153*^9}, {3.815392331888154*^9, 3.8153923784440737`*^9}, { + 3.8153936463145723`*^9, 3.815393697746064*^9}, {3.815393812205121*^9, + 3.81539384621247*^9}, {3.815393966073359*^9, 3.8153939668836193`*^9}, { + 3.81539403806533*^9, 3.8153940394984837`*^9}, {3.8153940774792213`*^9, + 3.815394079181129*^9}, {3.8153941503791018`*^9, 3.815394151474286*^9}}, + CellLabel-> + "In[323]:=",ExpressionUUID->"5b1fe8b5-3e89-480f-b5a5-40f18f8383d3"], + +Cell[BoxData[ + RowBox[{"-", "1"}]], "Output", + CellChangeTimes->{{3.815393683029578*^9, 3.815393700465582*^9}, { + 3.815393825947748*^9, 3.8153938501911182`*^9}, 3.815393970673094*^9, + 3.815394043005232*^9, 3.8153940809159403`*^9, 3.815394154659795*^9}, + CellLabel-> + "Out[324]=",ExpressionUUID->"ba1698ac-3e78-478d-ac5b-ebfbf797bcd4"] +}, Open ]], + +Cell["Using up to MP4 gives...", "Text", + CellChangeTimes->{{3.815392554679447*^9, + 3.815392568663185*^9}},ExpressionUUID->"2c9794aa-5115-4ffd-abd4-\ +dee83f70c74b"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"With", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"MPorder", "=", "4"}], "}"}], ",", "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Print", "[", + RowBox[{ + RowBox[{ + RowBox[{"CumUMP", "\[LeftDoubleBracket]", + RowBox[{"MPorder", "+", "1"}], "\[RightDoubleBracket]"}], "/", + "Eexact"}], "*", "100."}], "]"}], ";", "\[IndentingNewLine]", + RowBox[{"Print", "[", + RowBox[{ + RowBox[{ + RowBox[{ + "Richardson1", "\[LeftDoubleBracket]", "MPorder", + "\[RightDoubleBracket]"}], "/", "Eexact"}], "*", "100."}], "]"}], ";", + "\[IndentingNewLine]", + RowBox[{"Print", "[", + RowBox[{ + RowBox[{ + RowBox[{"Richardson2", "\[LeftDoubleBracket]", + RowBox[{"MPorder", "-", "1"}], "\[RightDoubleBracket]"}], "/", + "Eexact"}], "*", "100."}], "]"}], ";"}]}], "]"}]], "Input", + CellChangeTimes->{{3.815392575359654*^9, 3.815392636238756*^9}, { + 3.815392710994277*^9, 3.815392750836833*^9}, {3.815392799446349*^9, + 3.815392879650866*^9}, {3.815393707185802*^9, 3.81539370749372*^9}, { + 3.815393934502144*^9, 3.815393950587875*^9}, {3.815394002357135*^9, + 3.815394031068569*^9}, {3.8153940625544033`*^9, 3.815394092087304*^9}, { + 3.815394171474327*^9, 3.815394174578247*^9}}, + CellLabel-> + "In[330]:=",ExpressionUUID->"ae85fc45-30a7-49e0-a96d-3e8f5db7dad6"], + +Cell[CellGroupData[{ + +Cell[BoxData["82.21307727480567`"], "Print", + CellChangeTimes->{{3.8153928631837187`*^9, 3.8153928799129877`*^9}, + 3.815393708143965*^9, {3.815393934729683*^9, 3.815394086536972*^9}, { + 3.815394156451034*^9, 3.8153941748593483`*^9}}, + CellLabel-> + "During evaluation of \ +In[330]:=",ExpressionUUID->"1c025698-7705-4895-b6dd-ea73a38a9fa6"], + +Cell[BoxData["98.30818472793781`"], "Print", + CellChangeTimes->{{3.8153928631837187`*^9, 3.8153928799129877`*^9}, + 3.815393708143965*^9, {3.815393934729683*^9, 3.815394086536972*^9}, { + 3.815394156451034*^9, 3.815394174860847*^9}}, + CellLabel-> + "During evaluation of \ +In[330]:=",ExpressionUUID->"d4a015e5-300d-4c2f-8155-40d7237d9455"], + +Cell[BoxData["109.96799268404207`"], "Print", + CellChangeTimes->{{3.8153928631837187`*^9, 3.8153928799129877`*^9}, + 3.815393708143965*^9, {3.815393934729683*^9, 3.815394086536972*^9}, { + 3.815394156451034*^9, 3.815394174863255*^9}}, + CellLabel-> + "During evaluation of \ +In[330]:=",ExpressionUUID->"4bcb8014-aaf0-4622-a7bf-d5e29900c1d3"] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ListPlot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"MPorder", "-", "1"}], ",", + RowBox[{ + RowBox[{ + "CumUMP", "\[LeftDoubleBracket]", "MPorder", + "\[RightDoubleBracket]"}], "/", "Eexact"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"MPorder", ",", "1", ",", "20"}], "}"}]}], "]"}], ",", + "\[IndentingNewLine]", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"MPorder", ",", + RowBox[{ + RowBox[{ + "Richardson1", "\[LeftDoubleBracket]", "MPorder", + "\[RightDoubleBracket]"}], "/", "Eexact"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"MPorder", ",", "1", ",", "20"}], "}"}]}], "]"}], ",", + "\[IndentingNewLine]", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"MPorder", "+", "1"}], ",", + RowBox[{ + RowBox[{ + "Richardson2", "\[LeftDoubleBracket]", "MPorder", + "\[RightDoubleBracket]"}], "/", "Eexact"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"MPorder", ",", "1", ",", "20"}], "}"}]}], "]"}]}], "}"}], + ",", "\[IndentingNewLine]", + RowBox[{"Joined", "\[Rule]", "True"}], ",", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", + RowBox[{"Red", ",", "Green", ",", "Blue"}], "}"}]}], ",", + RowBox[{"PlotRange", "\[Rule]", + RowBox[{"{", + RowBox[{"0", ",", "2"}], "}"}]}]}], "]"}]], "Input", + CellChangeTimes->{{3.815392892853909*^9, 3.815393100775874*^9}, { + 3.815393238049349*^9, 3.815393240475934*^9}, {3.8153933879821672`*^9, + 3.815393412083436*^9}, 3.8153937638247967`*^9, {3.815393903566483*^9, + 3.815393905813622*^9}, {3.8153941036185293`*^9, 3.815394117255843*^9}}, + CellLabel-> + "In[322]:=",ExpressionUUID->"9274b79e-b9ac-48d1-85d1-0fe707abc4cb"], + +Cell[BoxData[ + GraphicsBox[{{}, {{{}, {}, + {RGBColor[1, 0, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6], LineBox[CompressedData[" +1:eJxTTMoPSmViYGAQAWIQjR18sF/xZfrs8scv7aECDi9/2B3U0vsA5XOg8QUc +/k/kX3L8y3soXwSNL+Hwd9279XcYYOpl0PgKDlJmrbM2/4epV0LjqziEvw6W +ZoerV0PjazhMiki0/AtXr4XG13G48PCmOwNcvR4a38DhEav2o/9w9YZofCOH +rWKazAj1xnA+AAFsWz0= + "]]}, + {RGBColor[0, 1, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6], LineBox[CompressedData[" +1:eJxTTMoPSmViYGAQAWIQDQEf7Fd8mT67/PFPe6iAg/A3lRUcy79B+RwOL3/Y +HdTS+wDlCzhsFQrTmhD2DsoXcfg/kX/J8S/voXwJhzdCEY83qsPUyzj8Xfdu +/R0GGF/BQfH74fzW9zD1Sg5SZq2zNv+H8VUcrPgYNc4wwtSrOYS/DpZmh+vX +cHDLF44yhKvXcpgUkWj5F87XcTA/L7VEHK5ez+HCw5vuDHC+gcNnzfmcX+Hq +DR0esWo/+g/nGzlUV3V6MMLVGztsFdNkRug3cWDi/ZsCUg8AXK5bYA== + "]]}, + {RGBColor[0, 0, 1], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6], LineBox[CompressedData[" +1:eJxTTMoPSmViYGAQAWIQDQUOJ8qy9S5yfLWHcDkc6r5v3DIz6zGUL+DA6SKl +9sL3NZQv4uDlcdB79oyPUL6Ew67TC/i+zvgA5cs4JLClau+SeA/lKzjo8mcv +P78exldy+C9xVMlMAaZexaFVJOpAHxeMr+ZwrvLJ9uh3MPUaDh1mj+cU/YLx +tRz0M2ZZJTHB1Os42G3yCdnFAOPrOXCfUGvZ+Q+m3sAhfCXLnHn/YXxDh/Wf +XIK14eqNHCYYPV7PA+cbO9Rqdqu+hKs3cdCODMn4CeebOrQfmvifCageAHy/ +WaY= + "]]}}, { + {RGBColor[1, 0, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 1, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 0, 1], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}}, { + {RGBColor[1, 0, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 1, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 0, 1], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, {}, {}, {}, {}, {}, {}, {}}, { + {RGBColor[1, 0, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 1, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 0, 1], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, {}, {}, {}, {}, {}, {}, {}}}, {{}, {}}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 0}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImageSize->{623., Automatic}, + Method->{ + "OptimizePlotMarkers" -> True, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{0, 21.}, {0, 2}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, {0, 0}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{{3.815392919646822*^9, 3.81539295556921*^9}, { + 3.815393041766121*^9, 3.815393047848632*^9}, {3.8153930801732893`*^9, + 3.815393101236308*^9}, {3.815393238736053*^9, 3.8153932410334997`*^9}, + 3.8153934127365103`*^9, 3.8153936576986856`*^9, 3.81539371673884*^9, + 3.815393764186681*^9, 3.815393827830627*^9, 3.815393858076087*^9, + 3.815393906611137*^9, 3.815393981138159*^9, 3.8153940496803427`*^9, { + 3.815394097596229*^9, 3.815394117753169*^9}}, + CellLabel-> + "Out[322]=",ExpressionUUID->"9bf35615-22b3-46e3-8342-2f2d9aa66ca2"] +}, Open ]], + +Cell[BoxData[ + RowBox[{"\[IndentingNewLine]", + RowBox[{ + RowBox[{ + RowBox[{"RMPseries", "=", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"SeriesCoefficient", "[", + RowBox[{ + RowBox[{ + RowBox[{ + FractionBox["1", "2"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"2", " ", "U"}], "-", + RowBox[{"U", " ", "\[Lambda]"}], "-", + SqrtBox[ + RowBox[{ + RowBox[{"16", " ", + SuperscriptBox["t", "2"]}], "+", + RowBox[{ + SuperscriptBox["U", "2"], " ", + SuperscriptBox["\[Lambda]", "2"]}]}]]}], ")"}]}], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"U", "\[Rule]", "3"}], ",", + RowBox[{"t", "\[Rule]", "1"}]}], "}"}]}], ",", + RowBox[{"{", + RowBox[{"\[Lambda]", ",", "0", ",", "i"}], "}"}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"i", ",", "0", ",", "100"}], "}"}]}], "]"}]}], ";"}], + "\[IndentingNewLine]", + RowBox[{ + RowBox[{"CumRMP", "=", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"Sum", "[", + RowBox[{ + RowBox[{ + "RMPseries", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], + ",", + RowBox[{"{", + RowBox[{"i", ",", "1", ",", "x"}], "}"}]}], "]"}], ",", + RowBox[{"{", + RowBox[{"x", ",", "1", ",", "100"}], "}"}]}], "]"}]}], + ";"}]}]}]], "Input", + CellChangeTimes->{{3.81539329219571*^9, 3.815393305276984*^9}, + 3.8153935233653593`*^9}, + CellLabel-> + "In[244]:=",ExpressionUUID->"5e463f22-a38c-4da7-b505-9911cc700f39"], + +Cell[BoxData[{ + RowBox[{ + RowBox[{"Shanks1", "=", + RowBox[{"Table", "[", + RowBox[{ + FractionBox[ + RowBox[{ + RowBox[{ + RowBox[{"CumRMP", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}], + RowBox[{"CumRMP", "\[LeftDoubleBracket]", + RowBox[{"n", "-", "1"}], "\[RightDoubleBracket]"}]}], "-", + SuperscriptBox[ + RowBox[{ + "CumRMP", "\[LeftDoubleBracket]", "n", "\[RightDoubleBracket]"}], + "2"]}], + RowBox[{ + RowBox[{"CumRMP", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}], "-", + RowBox[{"2", + RowBox[{ + "CumRMP", "\[LeftDoubleBracket]", "n", "\[RightDoubleBracket]"}]}], + "+", + RowBox[{"CumRMP", "\[LeftDoubleBracket]", + RowBox[{"n", "-", "1"}], "\[RightDoubleBracket]"}]}]], ",", + RowBox[{"{", + RowBox[{"n", ",", "2", ",", "48"}], "}"}]}], "]"}]}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Shanks2", "=", + RowBox[{"Table", "[", + RowBox[{ + FractionBox[ + RowBox[{ + RowBox[{ + RowBox[{"Shanks1", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}], + RowBox[{"Shanks1", "\[LeftDoubleBracket]", + RowBox[{"n", "-", "1"}], "\[RightDoubleBracket]"}]}], "-", + SuperscriptBox[ + RowBox[{ + "Shanks1", "\[LeftDoubleBracket]", "n", "\[RightDoubleBracket]"}], + "2"]}], + RowBox[{ + RowBox[{"Shanks1", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}], "-", + RowBox[{"2", + RowBox[{ + "Shanks1", "\[LeftDoubleBracket]", "n", "\[RightDoubleBracket]"}]}], + "+", + RowBox[{"Shanks1", "\[LeftDoubleBracket]", + RowBox[{"n", "-", "1"}], "\[RightDoubleBracket]"}]}]], ",", + RowBox[{"{", + RowBox[{"n", ",", "2", ",", "46"}], "}"}]}], "]"}]}], ";"}]}], "Input", + CellChangeTimes->{{3.815387621751258*^9, 3.815387714316226*^9}, + 3.815387851978386*^9, {3.815393126249597*^9, 3.8153932165429773`*^9}, { + 3.8153933091707087`*^9, 3.815393316981332*^9}, {3.815393424224601*^9, + 3.815393436322711*^9}}, + CellLabel-> + "In[246]:=",ExpressionUUID->"843caa0e-3907-4bab-b127-4f81a28921b4"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ListPlot", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"MPorder", "-", "1"}], ",", + RowBox[{ + RowBox[{ + "CumRMP", "\[LeftDoubleBracket]", "MPorder", + "\[RightDoubleBracket]"}], "/", "Eexact"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"MPorder", ",", "1", ",", "20"}], "}"}]}], "]"}], ",", + "\[IndentingNewLine]", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"MPorder", "+", "1"}], ",", + RowBox[{ + RowBox[{ + "Shanks1", "\[LeftDoubleBracket]", "MPorder", + "\[RightDoubleBracket]"}], "/", "Eexact"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"MPorder", ",", "1", ",", "20"}], "}"}]}], "]"}], ",", + "\[IndentingNewLine]", + RowBox[{"Table", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"MPorder", "+", "2"}], ",", + RowBox[{ + RowBox[{ + "Shanks2", "\[LeftDoubleBracket]", "MPorder", + "\[RightDoubleBracket]"}], "/", "Eexact"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"MPorder", ",", "1", ",", "20"}], "}"}]}], "]"}]}], "}"}], + ",", + RowBox[{"Joined", "\[Rule]", "True"}], ",", + RowBox[{"PlotStyle", "\[Rule]", + RowBox[{"{", + RowBox[{"Red", ",", "Green", ",", "Blue"}], "}"}]}]}], "]"}]], "Input", + CellChangeTimes->{{3.8153932198059053`*^9, 3.815393250576565*^9}, + 3.8153933200105247`*^9, {3.81539345035011*^9, 3.815393472026103*^9}, { + 3.815393510487772*^9, 3.815393540161022*^9}}, + CellLabel-> + "In[249]:=",ExpressionUUID->"cc354370-daa4-48e0-a72e-0d631558ce95"], + +Cell[BoxData[ + GraphicsBox[{{}, {{{}, {}, + {RGBColor[1, 0, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6], LineBox[{{5.042968750000007, 1.8533249173650717`}, {6., + 1.8934119399249356`}, {7., 1.8934119399249356`}, {8., + 1.8786860949029447`}, {9., 1.8786860949029447`}, {10., + 1.8844843963803537`}, {11., 1.8844843963803537`}, {12., + 1.8820382379445717`}, {13., 1.8820382379445717`}, {14., + 1.883119352610386}, {15., 1.883119352610386}, {16., + 1.8826252494232756`}, {17., 1.8826252494232756`}, {18., + 1.8828568602922335`}, {19., 1.8828568602922335`}}], + LineBox[{{1.861074447631836, 1.8533249173650717`}, {1.9197826385498045`, + 1.915500707457922}}], + LineBox[{{3.570434570312501, 1.915500707457922}, {3.987915039062498, + 1.8533249173650717`}}]}, + {RGBColor[0, 1, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6], LineBox[{{6.042968750000007, 1.8533249173650717`}, {7., + 1.8934119399249356`}, {8., 1.8934119399249356`}, {9., + 1.8786860949029447`}, {10., 1.8786860949029447`}, {11., + 1.8844843963803537`}, {12., 1.8844843963803537`}, {13., + 1.8820382379445717`}, {14., 1.8820382379445717`}, {15., + 1.883119352610386}, {16., 1.883119352610386}, {17., + 1.8826252494232756`}, {18., 1.8826252494232756`}, {19., + 1.8828568602922335`}, {20., 1.8828568602922335`}, {21., + 1.882746121345513}}], + LineBox[{{4.570434570312501, 1.915500707457922}, {4.987915039062498, + 1.8533249173650717`}}]}, + {RGBColor[0, 0, 1], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6], LineBox[{{6.042968750000007, 1.8533249173650717`}, {7., + 1.8934119399249356`}, {8., 1.8934119399249356`}, {9., + 1.8786860949029447`}, {10., 1.8786860949029447`}, {11., + 1.8844843963803537`}, {12., 1.8844843963803537`}, {13., + 1.8820382379445717`}, {14., 1.8820382379445717`}, {15., + 1.883119352610386}, {16., 1.883119352610386}, {17., + 1.8826252494232756`}, {18., 1.8826252494232756`}, {19., + 1.8828568602922335`}, {20., 1.8828568602922335`}, {21., + 1.882746121345513}, {22., 1.882746121345513}}], + LineBox[{{4.570434570312501, 1.915500707457922}, {4.987915039062498, + 1.8533249173650717`}}]}}, { + {RGBColor[1, 0, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 1, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 0, 1], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}}, { + {RGBColor[1, 0, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 1, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 0, 1], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, {}, {}, {}, {}, {}, {}, {}}, { + {RGBColor[1, 0, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 1, 0], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, + {RGBColor[0, 0, 1], PointSize[0.011000000000000001`], AbsoluteThickness[ + 1.6]}, {}, {}, {}, {}, {}, {}, {}}}, {{}, {}}}, + AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], + Axes->{True, True}, + AxesLabel->{None, None}, + AxesOrigin->{0, 1.8533249173650717`}, + DisplayFunction->Identity, + Frame->{{False, False}, {False, False}}, + FrameLabel->{{None, None}, {None, None}}, + FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, + GridLines->{None, None}, + GridLinesStyle->Directive[ + GrayLevel[0.5, 0.4]], + ImageSize->{895., Automatic}, + Method->{ + "OptimizePlotMarkers" -> True, + "CoordinatesToolOptions" -> {"DisplayFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& ), "CopiedValueFunction" -> ({ + (Identity[#]& )[ + Part[#, 1]], + (Identity[#]& )[ + Part[#, 2]]}& )}}, + PlotRange->{{0, 22.}, {1.8533249173650717`, 1.915500707457922}}, + PlotRangeClipping->True, + PlotRangePadding->{{ + Scaled[0.02], + Scaled[0.02]}, { + Scaled[0.05], + Scaled[0.05]}}, + Ticks->{Automatic, Automatic}]], "Output", + CellChangeTimes->{{3.815393225187017*^9, 3.815393251080804*^9}, + 3.815393325404529*^9, {3.8153934994290524`*^9, 3.815393540788312*^9}}, + CellLabel-> + "Out[249]=",ExpressionUUID->"f63e1959-ac88-4d24-833c-2dbbfd9b2121"] +}, Open ]], + +Cell[BoxData[{ + RowBox[{ + RowBox[{"Shanks1", "=", + RowBox[{"Table", "[", + RowBox[{ + FractionBox[ + RowBox[{ + RowBox[{ + RowBox[{"UMPseries", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}], + RowBox[{"UMPseries", "\[LeftDoubleBracket]", + RowBox[{"n", "-", "1"}], "\[RightDoubleBracket]"}]}], "-", + SuperscriptBox[ + RowBox[{ + "UMPseries", "\[LeftDoubleBracket]", "n", "\[RightDoubleBracket]"}], + "2"]}], + RowBox[{ + RowBox[{"UMPseries", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}], "-", + RowBox[{"2", + RowBox[{ + "UMPseries", "\[LeftDoubleBracket]", "n", "\[RightDoubleBracket]"}]}], + "+", + RowBox[{"UMPseries", "\[LeftDoubleBracket]", + RowBox[{"n", "-", "1"}], "\[RightDoubleBracket]"}]}]], ",", + RowBox[{"{", + RowBox[{"n", ",", "2", ",", "48"}], "}"}]}], "]"}]}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Shanks2", "=", + RowBox[{"Table", "[", + RowBox[{ + FractionBox[ + RowBox[{ + RowBox[{ + RowBox[{"Shanks1", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}], + RowBox[{"Shanks1", "\[LeftDoubleBracket]", + RowBox[{"n", "-", "1"}], "\[RightDoubleBracket]"}]}], "-", + SuperscriptBox[ + RowBox[{ + "Shanks1", "\[LeftDoubleBracket]", "n", "\[RightDoubleBracket]"}], + "2"]}], + RowBox[{ + RowBox[{"Shanks1", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}], "-", + RowBox[{"2", + RowBox[{ + "Shanks1", "\[LeftDoubleBracket]", "n", "\[RightDoubleBracket]"}]}], + "+", + RowBox[{"Shanks1", "\[LeftDoubleBracket]", + RowBox[{"n", "-", "1"}], "\[RightDoubleBracket]"}]}]], ",", + RowBox[{"{", + RowBox[{"n", ",", "2", ",", "46"}], "}"}]}], "]"}]}], + ";"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"Shanks3", "=", + RowBox[{"Table", "[", + RowBox[{ + FractionBox[ + RowBox[{ + RowBox[{ + RowBox[{"Shanks2", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}], + RowBox[{"Shanks2", "\[LeftDoubleBracket]", + RowBox[{"n", "-", "1"}], "\[RightDoubleBracket]"}]}], "-", + SuperscriptBox[ + RowBox[{ + "Shanks2", "\[LeftDoubleBracket]", "n", "\[RightDoubleBracket]"}], + "2"]}], + RowBox[{ + RowBox[{"Shanks2", "\[LeftDoubleBracket]", + RowBox[{"n", "+", "1"}], "\[RightDoubleBracket]"}], "-", + RowBox[{"2", + RowBox[{ + "Shanks2", "\[LeftDoubleBracket]", "n", "\[RightDoubleBracket]"}]}], + "+", + RowBox[{"Shanks2", "\[LeftDoubleBracket]", + RowBox[{"n", "-", "1"}], "\[RightDoubleBracket]"}]}]], ",", + RowBox[{"{", + RowBox[{"n", ",", "2", ",", "44"}], "}"}]}], "]"}]}], ";"}]}], "Input", + CellChangeTimes->{{3.815387724872158*^9, 3.8153877389845257`*^9}, { + 3.815387807354072*^9, 3.8153878198147907`*^9}, {3.81538785401007*^9, + 3.815387859603508*^9}}, + CellLabel->"In[25]:=",ExpressionUUID->"41fd74a7-2531-4582-b5db-f928a258b277"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"PadeApproximant", "[", + RowBox[{ + RowBox[{ + FractionBox[ + RowBox[{"Root", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"4", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "4"], " ", "\[Lambda]"}], "-", + RowBox[{"4", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "4"], " ", + SuperscriptBox["\[Lambda]", "2"]}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"2", " ", + SuperscriptBox["U", "4"]}], "-", + RowBox[{"8", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "2"], " ", "\[Lambda]"}], "-", + RowBox[{"2", " ", + SuperscriptBox["U", "4"], " ", "\[Lambda]"}], "+", + RowBox[{"4", " ", + SuperscriptBox["t", "2"], " ", + SuperscriptBox["U", "2"], " ", + SuperscriptBox["\[Lambda]", "2"]}]}], ")"}], " ", "#1"}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"-", "3"}], " ", + SuperscriptBox["U", "2"]}], "+", + RowBox[{"2", " ", + SuperscriptBox["U", "2"], " ", "\[Lambda]"}]}], ")"}], " ", + SuperscriptBox["#1", "2"]}], "+", + SuperscriptBox["#1", "3"]}], "&"}], ",", "1"}], "]"}], "U"], "/.", + RowBox[{"{", + RowBox[{ + RowBox[{"U", "\[Rule]", "7"}], ",", + RowBox[{"t", "\[Rule]", "1"}]}], "}"}]}], ",", + RowBox[{"{", + RowBox[{"\[Lambda]", ",", "0", ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], "]"}]], "Input", + CellChangeTimes->{{3.815391403967659*^9, 3.815391429427579*^9}}, + CellLabel->"In[29]:=",ExpressionUUID->"368d0b5c-7e30-4f0f-8181-678d4c4f92c3"], + +Cell[BoxData[ + RowBox[{"-", + FractionBox[ + RowBox[{"2", " ", "\[Lambda]"}], + RowBox[{"7", " ", + RowBox[{"(", + RowBox[{"1", "-", + FractionBox["\[Lambda]", "49"]}], ")"}]}]]}]], "Output", + CellChangeTimes->{3.8153914299511957`*^9}, + CellLabel->"Out[29]=",ExpressionUUID->"746b040c-1484-426a-b4f0-995afc93f19b"] }, Open ]] }, Open ]] }, -WindowSize->{1440, 752}, -WindowMargins->{{110, Automatic}, {91, Automatic}}, +WindowSize->{1426, 752}, +WindowMargins->{{206, Automatic}, {Automatic, 133}}, FrontEndVersion->"12.0 for Linux x86 (64-bit) (April 8, 2019)", StyleDefinitions->"Default.nb" ] @@ -120526,8 +121902,8 @@ Cell[CellGroupData[{ Cell[26826, 677, 158, 3, 54, "Section",ExpressionUUID->"82473538-3fcd-43de-ae6d-db82689febad"], Cell[26987, 682, 384, 10, 31, "Input",ExpressionUUID->"9a0654e9-c7db-45cf-a247-321b52f79c79"], Cell[CellGroupData[{ -Cell[27396, 696, 906, 30, 82, InheritFromParent,ExpressionUUID->"4e4c7411-4ad7-4921-9cda-3a753cb7b00c"], -Cell[28305, 728, 641, 22, 98, "Output",ExpressionUUID->"0408d0c0-4a57-4bf4-ada8-f8409a8e43a9"] +Cell[27396, 696, 906, 30, 82, "Input",ExpressionUUID->"4e4c7411-4ad7-4921-9cda-3a753cb7b00c"], +Cell[28305, 728, 641, 22, 41, "Output",ExpressionUUID->"0408d0c0-4a57-4bf4-ada8-f8409a8e43a9"] }, Open ]], Cell[28961, 753, 408, 6, 36, "Text",ExpressionUUID->"5a3229c5-e906-4dc5-8802-485747752fe7"], Cell[CellGroupData[{ @@ -120550,7 +121926,7 @@ Cell[35839, 955, 310, 8, 35, "Output",ExpressionUUID->"2f05e3b4-b816-454a-8fb0-9 }, Open ]], Cell[36164, 966, 348, 6, 60, "Text",ExpressionUUID->"dd898830-e31f-4772-97b0-fda2ee57ee09"], Cell[CellGroupData[{ -Cell[36537, 976, 3747, 92, 181, "Input",ExpressionUUID->"4de7e9d1-be22-47f0-a628-16256e17ba60"], +Cell[36537, 976, 3747, 92, 204, "Input",ExpressionUUID->"4de7e9d1-be22-47f0-a628-16256e17ba60"], Cell[40287, 1070, 83800, 1607, 438, "Output",ExpressionUUID->"36486767-5c66-458b-984c-07218d82fffe"] }, Open ]], Cell[CellGroupData[{ @@ -120566,10 +121942,10 @@ Cell[354274, 6548, 487, 12, 48, "Input",ExpressionUUID->"61531a40-1ab8-44ab-a9fb Cell[354764, 6562, 622, 16, 53, "Output",ExpressionUUID->"9bd3543a-8b55-45ae-924d-780045a6d1cc"] }, Open ]], Cell[CellGroupData[{ -Cell[355423, 6583, 2046, 54, 49, "Input",ExpressionUUID->"4dd16f37-8c37-45ed-80ba-dd65ec31d7a8"], -Cell[357472, 6639, 4697, 147, 119, "Output",ExpressionUUID->"4c1e68b2-23d5-4e02-9db6-97fde8b6176e"] +Cell[355423, 6583, 2046, 54, 73, "Input",ExpressionUUID->"4dd16f37-8c37-45ed-80ba-dd65ec31d7a8"], +Cell[357472, 6639, 4697, 147, 159, "Output",ExpressionUUID->"4c1e68b2-23d5-4e02-9db6-97fde8b6176e"] }, Open ]], -Cell[362184, 6789, 5326, 159, 160, "Input",ExpressionUUID->"72223883-4ec4-4ef3-a96f-05390dbf9247"], +Cell[362184, 6789, 5326, 159, 218, "Input",ExpressionUUID->"72223883-4ec4-4ef3-a96f-05390dbf9247"], Cell[CellGroupData[{ Cell[367535, 6952, 874, 22, 49, "Input",ExpressionUUID->"45b3bf2c-8df5-4cd8-a499-f7021cdb25bd"], Cell[368412, 6976, 1087, 35, 58, "Output",ExpressionUUID->"4ac581f2-80df-471c-aaac-c16b3cdaf1c9"] @@ -120641,13 +122017,13 @@ Cell[2874203, 53915, 79689, 1498, 428, "Output",ExpressionUUID->"3181322c-be4a-4 }, Open ]], Cell[2953907, 55416, 317, 5, 36, "Text",ExpressionUUID->"5c754450-1b09-4800-bcc0-9052c82f8a81"], Cell[CellGroupData[{ -Cell[2954249, 55425, 6600, 167, 364, "Input",ExpressionUUID->"c68d16b8-ddf2-4ed4-88c2-e682495595d7"], +Cell[2954249, 55425, 6600, 167, 387, "Input",ExpressionUUID->"c68d16b8-ddf2-4ed4-88c2-e682495595d7"], Cell[2960852, 55594, 385704, 6371, 577, 147770, 2470, "CachedBoxData", "BoxData", "Output",ExpressionUUID->"673148aa-d9dd-48bc-b4ff-3ceaa38d4fee"] }, Open ]], Cell[3346571, 61968, 154, 3, 31, "Input",ExpressionUUID->"4ed9b9f2-9a0c-4a9d-b7da-6aef05e7dcad"], Cell[3346728, 61973, 152, 3, 31, "Input",ExpressionUUID->"66339502-9d62-4d8b-8698-b21b86842a75"], Cell[CellGroupData[{ -Cell[3346905, 61980, 6685, 167, 388, "Input",ExpressionUUID->"4259ed50-c390-40a9-957e-aa8bae6464ff"], +Cell[3346905, 61980, 6685, 167, 411, "Input",ExpressionUUID->"4259ed50-c390-40a9-957e-aa8bae6464ff"], Cell[3353593, 62149, 403198, 6654, 556, 159627, 2661, "CachedBoxData", "BoxData", "Output",ExpressionUUID->"600380b8-2ea1-4d1d-b0fa-743ea99d8dbe"] }, Open ]], Cell[CellGroupData[{ @@ -120670,9 +122046,9 @@ Cell[3762003, 68958, 2985, 91, 183, "Output",ExpressionUUID->"46edaaf4-6210-4097 Cell[3765003, 69052, 520, 8, 60, "Text",ExpressionUUID->"a5ef3f43-7b1a-40f7-bc5e-3884a79db05d"], Cell[CellGroupData[{ Cell[3765548, 69064, 3464, 95, 167, "Input",ExpressionUUID->"af7c449f-e708-4dec-9a95-e2a226c7965a"], -Cell[3769015, 69161, 19689, 536, 589, "Output",ExpressionUUID->"b0e836df-80be-4362-8e71-80b19b38dba8"] +Cell[3769015, 69161, 19689, 536, 678, "Output",ExpressionUUID->"b0e836df-80be-4362-8e71-80b19b38dba8"] }, Open ]], -Cell[3788719, 69700, 20541, 535, 573, "Input",ExpressionUUID->"2fb4d73f-58eb-41c5-8b49-bf0fd006c5c0"], +Cell[3788719, 69700, 20541, 535, 747, "Input",ExpressionUUID->"2fb4d73f-58eb-41c5-8b49-bf0fd006c5c0"], Cell[3809263, 70237, 547, 8, 84, "Text",ExpressionUUID->"5398c3b2-d083-4063-bf47-7124d8ed3084"], Cell[3809813, 70247, 4750, 121, 188, "Input",ExpressionUUID->"1120755f-bdd0-4db6-b62e-c8ce52edcbf1"], Cell[CellGroupData[{ @@ -120682,25 +122058,25 @@ Cell[CellGroupData[{ Cell[3815108, 70386, 177, 3, 46, "Subsubsection",ExpressionUUID->"87aeb388-e717-4e85-afe9-385f2f418096"], Cell[3815288, 70391, 615, 9, 84, "Text",ExpressionUUID->"96ec60cc-3a71-4407-b2a0-6a68cf68aaf7"], Cell[CellGroupData[{ -Cell[3815928, 70404, 6737, 167, 308, "Input",ExpressionUUID->"72eece5e-69b7-479f-b6f2-57f7b447924e"], +Cell[3815928, 70404, 6737, 167, 370, "Input",ExpressionUUID->"72eece5e-69b7-479f-b6f2-57f7b447924e"], Cell[3822668, 70573, 127346, 2366, 459, "Output",ExpressionUUID->"86537cfb-059f-4cd8-be81-104e58f67275"] }, Open ]], Cell[CellGroupData[{ -Cell[3950051, 72944, 7175, 173, 339, "Input",ExpressionUUID->"1f6626fd-ad7d-48ac-93e2-72ebe0bf57c2"], +Cell[3950051, 72944, 7175, 173, 370, "Input",ExpressionUUID->"1f6626fd-ad7d-48ac-93e2-72ebe0bf57c2"], Cell[3957229, 73119, 106124, 1985, 449, "Output",ExpressionUUID->"9f671c8d-e804-4baf-b83a-f1bfd33fd4e7"] }, Open ]], Cell[CellGroupData[{ Cell[4063390, 75109, 593, 12, 31, "Input",ExpressionUUID->"00c53a59-8d5d-4b7a-9bcc-6097736e8579"], Cell[4063986, 75123, 504, 12, 23, "Message",ExpressionUUID->"f675c9d7-20d1-4ec0-b213-43b4667c68b3"], -Cell[4064493, 75137, 106114, 1987, 469, "Output",ExpressionUUID->"a3d37b58-96f0-42a9-988f-2544b5907f1d"] +Cell[4064493, 75137, 106114, 1987, 436, "Output",ExpressionUUID->"a3d37b58-96f0-42a9-988f-2544b5907f1d"] }, Open ]], Cell[CellGroupData[{ Cell[4170644, 77129, 8535, 214, 569, "Input",ExpressionUUID->"a3f8fa43-8f60-4682-b612-a9217e1e7f2d"], Cell[4179182, 77345, 78015, 1474, 439, "Output",ExpressionUUID->"32dfbfee-fa98-4d48-bf4e-c5ddc1dbd5ca"], -Cell[4257200, 78821, 78149, 1462, 469, "Output",ExpressionUUID->"49f76475-7d72-4b2e-b354-14125c3272d5"] +Cell[4257200, 78821, 78149, 1462, 436, "Output",ExpressionUUID->"49f76475-7d72-4b2e-b354-14125c3272d5"] }, Open ]], Cell[CellGroupData[{ -Cell[4335386, 80288, 4284, 107, 395, "Input",ExpressionUUID->"89aacab6-cc1d-40e4-b5df-7f8c4eb71d3c"], +Cell[4335386, 80288, 4284, 107, 289, "Input",ExpressionUUID->"89aacab6-cc1d-40e4-b5df-7f8c4eb71d3c"], Cell[4339673, 80397, 77305, 1447, 453, "Output",ExpressionUUID->"936221d6-2c44-467a-988c-880a99e48c17"] }, Open ]] }, Open ]], @@ -120708,51 +122084,93 @@ Cell[CellGroupData[{ Cell[4417027, 81850, 181, 3, 46, "Subsubsection",ExpressionUUID->"6262f130-07d2-49f4-8990-db089589021f"], Cell[4417211, 81855, 400, 6, 60, "Text",ExpressionUUID->"f7218a51-6ba0-46a1-94d4-eac08b273c62"], Cell[CellGroupData[{ -Cell[4417636, 81865, 6988, 173, 603, "Input",ExpressionUUID->"4943dd3f-0811-4c76-9e70-3d37f6d5006f"], +Cell[4417636, 81865, 6988, 173, 377, "Input",ExpressionUUID->"4943dd3f-0811-4c76-9e70-3d37f6d5006f"], Cell[4424627, 82040, 109993, 2042, 442, "Output",ExpressionUUID->"4e37242e-2f9a-4545-9032-8ab412b5cae6"] }, Open ]] }, Open ]], Cell[CellGroupData[{ -Cell[4534669, 84088, 182, 3, 45, "Subsubsection",ExpressionUUID->"e71df111-b9c0-4fcb-a9d1-d6b16b02676a"], -Cell[4534854, 84093, 612, 9, 81, "Text",ExpressionUUID->"77a3d959-22f6-4251-9ded-781e16688ac1"], +Cell[4534669, 84088, 182, 3, 46, "Subsubsection",ExpressionUUID->"e71df111-b9c0-4fcb-a9d1-d6b16b02676a"], +Cell[4534854, 84093, 612, 9, 84, "Text",ExpressionUUID->"77a3d959-22f6-4251-9ded-781e16688ac1"], Cell[CellGroupData[{ -Cell[4535491, 84106, 7109, 174, 285, "Input",ExpressionUUID->"53291c95-01a4-4ec5-95f9-fda312a1f585"], -Cell[4542603, 84282, 109077, 2024, 441, "Output",ExpressionUUID->"5086d734-903c-42b0-9a32-753e369a9d15"] +Cell[4535491, 84106, 7109, 174, 377, "Input",ExpressionUUID->"53291c95-01a4-4ec5-95f9-fda312a1f585"], +Cell[4542603, 84282, 109077, 2024, 442, "Output",ExpressionUUID->"5086d734-903c-42b0-9a32-753e369a9d15"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ -Cell[4651741, 86313, 269, 4, 54, "Subsection",ExpressionUUID->"88abadb0-1d05-421c-b4b3-14793c0012a1"], -Cell[4652013, 86319, 449, 7, 35, "Text",ExpressionUUID->"0a1530fa-55e8-44ea-8d84-88d4b1fd62fa"], +Cell[4651741, 86313, 269, 4, 55, "Subsection",ExpressionUUID->"88abadb0-1d05-421c-b4b3-14793c0012a1"], +Cell[4652013, 86319, 449, 7, 36, "Text",ExpressionUUID->"0a1530fa-55e8-44ea-8d84-88d4b1fd62fa"], Cell[CellGroupData[{ -Cell[4652487, 86330, 208, 4, 45, "Subsubsection",ExpressionUUID->"7622ddd0-a3ff-4d4b-b73e-3215ff17337a"], -Cell[4652698, 86336, 1642, 23, 288, "Text",ExpressionUUID->"ead47e6e-2cb5-4d9b-a984-d08011c4950f"], -Cell[4654343, 86361, 2048, 55, 184, "Input",ExpressionUUID->"0b00d05d-2ec1-4d27-8811-b2d0e7c5ad74"], +Cell[4652487, 86330, 208, 4, 46, "Subsubsection",ExpressionUUID->"7622ddd0-a3ff-4d4b-b73e-3215ff17337a"], +Cell[4652698, 86336, 1642, 23, 300, "Text",ExpressionUUID->"ead47e6e-2cb5-4d9b-a984-d08011c4950f"], +Cell[4654343, 86361, 2048, 55, 199, "Input",ExpressionUUID->"0b00d05d-2ec1-4d27-8811-b2d0e7c5ad74"], Cell[CellGroupData[{ -Cell[4656416, 86420, 4497, 105, 296, "Input",ExpressionUUID->"d61acf55-1480-4c5a-9923-50bf417b3f76"], +Cell[4656416, 86420, 4497, 105, 321, "Input",ExpressionUUID->"d61acf55-1480-4c5a-9923-50bf417b3f76"], Cell[4660916, 86527, 1148853, 18888, 499, 972730, 16001, "CachedBoxData", "BoxData", "Output",ExpressionUUID->"d50be571-0f86-44a3-8622-8f155cc25fa5"] }, Open ]] }, Open ]], Cell[CellGroupData[{ -Cell[5809818, 105421, 182, 3, 45, "Subsubsection",ExpressionUUID->"15c444d1-fa26-43c5-84a4-246e5de0c8ed"], -Cell[5810003, 105426, 751, 11, 127, "Text",ExpressionUUID->"a332f586-96f4-4001-827b-1319e53ac3b0"], +Cell[5809818, 105421, 182, 3, 46, "Subsubsection",ExpressionUUID->"15c444d1-fa26-43c5-84a4-246e5de0c8ed"], +Cell[5810003, 105426, 751, 11, 132, "Text",ExpressionUUID->"a332f586-96f4-4001-827b-1319e53ac3b0"], Cell[CellGroupData[{ -Cell[5810779, 105441, 4032, 100, 275, "Input",ExpressionUUID->"c7eb1c72-bdc6-4577-90fe-9b9777d50eef"], +Cell[5810779, 105441, 4032, 100, 297, "Input",ExpressionUUID->"c7eb1c72-bdc6-4577-90fe-9b9777d50eef"], Cell[5814814, 105543, 903533, 14859, 508, 681187, 11213, "CachedBoxData", "BoxData", "Output",ExpressionUUID->"dda8e76c-085c-4ef4-a2f8-ad287a24dfe0"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ -Cell[6718408, 120409, 185, 2, 54, "Subsection",ExpressionUUID->"682f5d84-4017-4e58-bb21-1f874ccd820f"], -Cell[6718596, 120413, 3126, 49, 587, "Text",ExpressionUUID->"9b51c24b-654d-48dc-878d-1415e41df166"] +Cell[6718408, 120409, 185, 2, 55, "Subsection",ExpressionUUID->"682f5d84-4017-4e58-bb21-1f874ccd820f"], +Cell[6718596, 120413, 3126, 49, 612, "Text",ExpressionUUID->"9b51c24b-654d-48dc-878d-1415e41df166"] }, Open ]] }, Open ]], Cell[CellGroupData[{ -Cell[6721771, 120468, 187, 3, 67, "Section",ExpressionUUID->"555b6565-ed9c-41db-8747-3eab70a65674"], -Cell[6721961, 120473, 69, 0, 35, "Text",ExpressionUUID->"c8622b61-f1b5-4100-9c90-7559df35a50a"], +Cell[6721771, 120468, 187, 3, 68, "Section",ExpressionUUID->"555b6565-ed9c-41db-8747-3eab70a65674"], +Cell[6721961, 120473, 69, 0, 36, "Text",ExpressionUUID->"c8622b61-f1b5-4100-9c90-7559df35a50a"], Cell[CellGroupData[{ -Cell[6722055, 120477, 428, 11, 51, "Input",ExpressionUUID->"be816819-a54c-429b-81a6-87e2bd4bddc9"], -Cell[6722486, 120490, 173, 2, 69, "Output",ExpressionUUID->"af287abc-d325-4b3d-b738-17f8150381b7"] +Cell[6722055, 120477, 428, 11, 54, "Input",ExpressionUUID->"be816819-a54c-429b-81a6-87e2bd4bddc9"], +Cell[6722486, 120490, 173, 2, 35, "Output",ExpressionUUID->"af287abc-d325-4b3d-b738-17f8150381b7"] +}, Open ]], +Cell[CellGroupData[{ +Cell[6722696, 120497, 251, 4, 31, "Input",ExpressionUUID->"78e9de6a-84d5-4c17-ad21-26acac8ce5b9"], +Cell[6722950, 120503, 7197, 171, 914, "Output",ExpressionUUID->"3018b4f4-0608-4636-83fb-d2661d7ae819"] +}, Open ]], +Cell[6730162, 120677, 1699, 45, 55, "Input",ExpressionUUID->"405dd260-566e-4a6b-963f-b2d59b93de2d"], +Cell[CellGroupData[{ +Cell[6731886, 120726, 320, 9, 49, InheritFromParent,ExpressionUUID->"72cdc13b-54ff-4fa8-b2ed-ba6038d95215"], +Cell[6732209, 120737, 188, 4, 35, "Output",ExpressionUUID->"5de04214-f291-4d6b-ac80-77c6ac510684"] +}, Open ]], +Cell[6732412, 120744, 229, 4, 31, "Input",ExpressionUUID->"28cd698a-a821-40fa-bd88-be3b282bfc34"], +Cell[CellGroupData[{ +Cell[6732666, 120752, 2320, 60, 147, "Input",ExpressionUUID->"3b3964cc-070a-4db7-9913-448b56d90c7b"], +Cell[6734989, 120814, 13362, 258, 566, "Output",ExpressionUUID->"d258cd3c-d761-4d87-9459-be86bc955d92"] +}, Open ]], +Cell[CellGroupData[{ +Cell[6748388, 121077, 6054, 164, 224, "Input",ExpressionUUID->"5b1fe8b5-3e89-480f-b5a5-40f18f8383d3"], +Cell[6754445, 121243, 340, 6, 35, "Output",ExpressionUUID->"ba1698ac-3e78-478d-ac5b-ebfbf797bcd4"] +}, Open ]], +Cell[6754800, 121252, 166, 3, 36, "Text",ExpressionUUID->"2c9794aa-5115-4ffd-abd4-dee83f70c74b"], +Cell[CellGroupData[{ +Cell[6754991, 121259, 1370, 32, 101, "Input",ExpressionUUID->"ae85fc45-30a7-49e0-a96d-3e8f5db7dad6"], +Cell[CellGroupData[{ +Cell[6756386, 121295, 344, 6, 25, "Print",ExpressionUUID->"1c025698-7705-4895-b6dd-ea73a38a9fa6"], +Cell[6756733, 121303, 342, 6, 25, "Print",ExpressionUUID->"d4a015e5-300d-4c2f-8155-40d7237d9455"], +Cell[6757078, 121311, 343, 6, 25, "Print",ExpressionUUID->"4bcb8014-aaf0-4622-a7bf-d5e29900c1d3"] +}, Open ]] +}, Open ]], +Cell[CellGroupData[{ +Cell[6757470, 121323, 1955, 52, 101, "Input",ExpressionUUID->"9274b79e-b9ac-48d1-85d1-0fe707abc4cb"], +Cell[6759428, 121377, 3650, 81, 421, "Output",ExpressionUUID->"9bf35615-22b3-46e3-8342-2f2d9aa66ca2"] +}, Open ]], +Cell[6763093, 121461, 1682, 49, 105, "Input",ExpressionUUID->"5e463f22-a38c-4da7-b505-9911cc700f39"], +Cell[6764778, 121512, 2291, 59, 108, "Input",ExpressionUUID->"843caa0e-3907-4bab-b127-4f81a28921b4"], +Cell[CellGroupData[{ +Cell[6767094, 121575, 1756, 49, 78, "Input",ExpressionUUID->"cc354370-daa4-48e0-a72e-0d631558ce95"], +Cell[6768853, 121626, 4473, 91, 571, "Output",ExpressionUUID->"f63e1959-ac88-4d24-833c-2dbbfd9b2121"] +}, Open ]], +Cell[6773341, 121720, 3217, 84, 159, "Input",ExpressionUUID->"41fd74a7-2531-4582-b5db-f928a258b277"], +Cell[CellGroupData[{ +Cell[6776583, 121808, 1846, 49, 55, "Input",ExpressionUUID->"368d0b5c-7e30-4f0f-8181-678d4c4f92c3"], +Cell[6778432, 121859, 330, 9, 63, "Output",ExpressionUUID->"746b040c-1484-426a-b4f0-995afc93f19b"] }, Open ]] }, Open ]] } diff --git a/References/Christiansen_1996.pdf b/References/Christiansen_1996.pdf new file mode 100644 index 0000000..aedb672 Binary files /dev/null and b/References/Christiansen_1996.pdf differ diff --git a/References/Fink_2016.pdf b/References/Fink_2016.pdf new file mode 100644 index 0000000..cc1459a Binary files /dev/null and b/References/Fink_2016.pdf differ diff --git a/References/Goodson_2000a.pdf b/References/Goodson_2000a.pdf new file mode 100644 index 0000000..a7de570 Binary files /dev/null and b/References/Goodson_2000a.pdf differ diff --git a/References/Goodson_2000b.pdf b/References/Goodson_2000b.pdf new file mode 100644 index 0000000..8754238 Binary files /dev/null and b/References/Goodson_2000b.pdf differ diff --git a/References/Goodson_2002.pdf b/References/Goodson_2002a.pdf similarity index 100% rename from References/Goodson_2002.pdf rename to References/Goodson_2002a.pdf diff --git a/References/Goodson_2002b.pdf b/References/Goodson_2002b.pdf new file mode 100644 index 0000000..d9cc41a Binary files /dev/null and b/References/Goodson_2002b.pdf differ diff --git a/References/Goodson_2006.pdf b/References/Goodson_2006.pdf new file mode 100644 index 0000000..f618cae Binary files /dev/null and b/References/Goodson_2006.pdf differ diff --git a/References/Herman_2008.pdf b/References/Herman_2008.pdf new file mode 100644 index 0000000..4f884b5 Binary files /dev/null and b/References/Herman_2008.pdf differ