Asymptotic expansion of

Author:
R. Wong

Journal:
Math. Comp. **50** (1988), 229-234

MSC:
Primary 41A60; Secondary 33A40

DOI:
https://doi.org/10.1090/S0025-5718-1988-0917830-2

MathSciNet review:
917830

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Abstract | References | Similar Articles | Additional Information

Abstract: An asymptotic expansion is obtained, as , for the integral

**[1]**N. Bleistein & R. A. Handelsman,*Asymptotic Expansions of Integrals*, Holt, Rinehart and Winston, New York, 1975.**[2]**B. C. Carlson & J. L. Gustafson, "Asymptotic expansion of the first elliptic integral,"*SIAM J. Math. Anal.*, v. 16, 1985, pp. 1072-1092. MR**800798 (87d:33002)****[3]**O. I. Marichev,*Handbook of Integral Transforms of Higher Transcendental Functions, Theory and Algorithmic Tables*, Ellis Horwood Ltd., West Sussex, England, 1983. MR**689711 (84f:00017)****[4]**F. W. J. Olver,*Asymptotics and Special Functions*, Academic Press, New York, 1974. MR**0435697 (55:8655)****[5]**B. J. Stoyanov &. R. A. Farrell, "On the asymptotic evaluation of ,"*Math. Comp.*, v. 49, 1987, pp. 275-279. MR**890269 (88e:41067)****[6]**R. Wong, "Explicit error terms for asymptotic expansions of Mellin convolutions,"*J. Math. Anal. Appl.*, v. 72, 1979, pp. 740-756. MR**559402 (81a:41049)****[7]**R. Wong, "Error bounds for asymptotic expansions of integrals,"*SIAM Rev.*, v. 22, 1980, pp. 401-435. MR**593856 (82a:41030)****[8]**R. Wong,*Applications of Some Recent Results in Asymptotic Expansions*, Proc. 12th Winnipeg Conf. on Numerical Methods of Computing,*Congress. Numer.*, v. 37, 1983, pp. 145-182. MR**703584 (84f:41031)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0917830-2

Keywords:
Asymptotic expansion,
Bessel functions,
Mellin transforms

Article copyright:
© Copyright 1988
American Mathematical Society