A double integral containing the modified Bessel function: asymptotics and computation

Author:
N. M. Temme

Journal:
Math. Comp. **47** (1986), 683-691

MSC:
Primary 33A40; Secondary 41A60, 65D30

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856712-X

MathSciNet review:
856712

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Abstract | References | Similar Articles | Additional Information

Abstract: A two-dimensional integral containing is considered. is the modified Bessel function and the integral is taken over the rectangle , . The integral is difficult to compute when *x* and *y* are large, especially when *x* and *y* are almost equal. Computer programs based on existing series expansions are inefficient in this case. A representation in terms of the error function (normal distribution function) is discussed, from which more efficient algorithms can be constructed.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856712-X

Keywords:
Bessel function integral,
uniform asymptotic expansion,
incomplete gamma functions

Article copyright:
© Copyright 1986
American Mathematical Society