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51 lines
1.1 KiB
Fortran
51 lines
1.1 KiB
Fortran
double precision function plgndr(l,m,x)
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integer, intent(in) :: l,m
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double precision, intent(in) :: x
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BEGIN_DOC
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! associated Legenre polynom P_l,m(x). Used for the Y_lm(theta,phi)
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! Taken from https://iate.oac.uncor.edu/~mario/materia/nr/numrec/f6-8.pdf
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END_DOC
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integer :: i,ll
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double precision :: fact,pll,pmm,pmmp1,somx2
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if(m.lt.0.or.m.gt.l.or.dabs(x).gt.1.d0)then
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print*,'bad arguments in plgndr'
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pause
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endif
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pmm=1.d0
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if(m.gt.0) then
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somx2=dsqrt((1.d0-x)*(1.d0+x))
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fact=1.d0
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do i=1,m
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pmm=-pmm*fact*somx2
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fact=fact+2.d0
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enddo
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endif ! m > 0
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if(l.eq.m) then
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plgndr=pmm
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else
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pmmp1=x*(2*m+1)*pmm ! Compute P_m+1^m
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if(l.eq.m+1) then
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plgndr=pmmp1
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else ! Compute P_l^m, l> m+1
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do ll=m+2,l
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pll=(x*dble(2*ll-1)*pmmp1-dble(ll+m-1)*pmm)/(ll-m)
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pmm=pmmp1
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pmmp1=pll
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enddo
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plgndr=pll
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endif ! l.eq.m+1
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endif ! l.eq.m
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return
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end
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double precision function ortho_assoc_gaus_pol(l1,m1,l2)
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implicit none
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integer, intent(in) :: l1,m1,l2
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double precision :: fact
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if(l1.ne.l2)then
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ortho_assoc_gaus_pol= 0.d0
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else
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ortho_assoc_gaus_pol = 2.d0*fact(l1+m1) / (dble(2*l1+1)*fact(l1-m1))
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endif
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end
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