On the computation of certain integrals containing the modified Bessel function $I_{0}(\xi )$

Author:
Keith R. Lassey

Journal:
Math. Comp. **39** (1982), 625-637

MSC:
Primary 65D20

DOI:
https://doi.org/10.1090/S0025-5718-1982-0669654-6

MathSciNet review:
669654

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Abstract: Efficient stratagems are developed for numerically evaluating one- and two-dimensional integrals over *x, y* with integrand $\exp ( - x - y){I_0}(2\sqrt {pxy} )$. The integrals are expressed in terms of convergent series, which exhibit the correct limiting behavior, and which can be evaluated recursively. The performances of these stratagems are compared with numerical integration.

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Additional Information

Keywords:
Modified Bessel functions,
integrals of Bessel functions,
recursive computation

Article copyright:
© Copyright 1982
American Mathematical Society