On the Computation of the Logarithm of the Modified Bessel Function of the Second Kind
Numerical Analysis
2023-08-24 v1 Numerical Analysis
Abstract
The modified Bessel function of the second kind K appears in a wide variety of applied scientific fields. While its use is greatly facilitated by an implementation in most numerical libraries, overflow issues can be encountered especially for large value of . After giving some necessary and sufficient conditions for their occurrences, this technical note shows that they can mostly be avoided by directly computing the logarithm of K thanks to a simple and stable forward recursion. A statistical examples based on the Gil-Pelaez inversion formula is given to illustrate the recursive method.
Keywords
Cite
@article{arxiv.2308.11964,
title = {On the Computation of the Logarithm of the Modified Bessel Function of the Second Kind},
author = {Remi Cuingnet},
journal= {arXiv preprint arXiv:2308.11964},
year = {2023}
}