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arXiv · 2308.11964

On the Computation of the Logarithm of the Modified Bessel Function of the Second Kind

Remi Cuingnet
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Abstract

The modified Bessel function of the second kind K$\nu$ 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 $\nu$. 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$\nu$ 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.

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Remi Cuingnet. 2023-08-23. On the Computation of the Logarithm of the Modified Bessel Function of the Second Kind. https://arxiv.org/abs/2308.11964

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