added small paragraph on singularities

This commit is contained in:
Pierre-Francois Loos 2020-11-28 22:16:36 +01:00
parent b1cd3ef2de
commit 17ef8dc9c1

View File

@ -194,7 +194,7 @@ We refer the interested reader to the excellent book of Moiseyev for a general o
\titou{Discussion around the different types of singularities in complex analysis.
At a singular point, a function and/or its derivatives becomes infinite or undefined (hence non analytic).
One very common type of singularities (belonging to the family of isolated singularities) are poles where the function behaves $1/(\lambda - \lambda_c)^n$ where $n \in \mathbb{N}^*$ is the order of the pole.
Another class of singularities are branch points resulting from a multi-valued function such as a square root or a logarithm function and usually implying the presence of so-called branch cuts where the function ``jumps'' from one value to another.
Another class of singularities are branch points resulting from a multi-valued function such as a square root or a logarithm function and usually implying the presence of so-called branch cuts which are lines or curves where the function ``jumps'' from one value to another.
Yet another family of singularities are formed by critical points which lie on the real axis, have more complicated functional forms and where the nature of the function undergoes a sudden transition.
}