A double integral containing the modified Bessel function: asymptotics and computation
Author:
N. M. Temme
Journal:
Math. Comp. 47 (1986), 683691
MSC:
Primary 33A40; Secondary 41A60, 65D30
MathSciNet review:
856712
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Abstract: A twodimensional 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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 D. E. Amos, "Computation of exponential integrals," ACM Trans. Math. Software, v. 6, 1980, pp. 365377. MR 585343 (82b:65011)
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 W. Gautschi, "Recursive computation of certain integrals," J. Assoc. Comput. Mach., v. 8, 1961, pp. 2140. MR 0119392 (22:10156)
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 C. G. Van Der Laan & N. M. Temme, Calculation of Special Functions: The Gamma Function, the Exponential Integrals and Errorlike Functions, CWI Tract 10, Centre for Mathematics and Computer Science, Amsterdam, 1984. MR 777869 (86g:65043)
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 F. W. J. Olver, Asymptotics and Special Functions, Academic Press, New York, 1974. MR 0435697 (55:8655)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819860856712X
PII:
S 00255718(1986)0856712X
Keywords:
Bessel function integral,
uniform asymptotic expansion,
incomplete gamma functions
Article copyright:
© Copyright 1986
American Mathematical Society
