On the Computation of the Logarithm of the Modified Bessel Function of the Second Kind
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The modified Bessel function of the second kind Kν 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 ν. 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 Kν 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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