An asymptotic approximation for a type of Fourier integral

Author:
Paul W. Schmidt

Journal:
Math. Comp. **32** (1978), 1171-1182

MSC:
Primary 41A60; Secondary 42A76

MathSciNet review:
0510821

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Abstract: A uniform asymptotic approximation which can be used for all is developed for the Fourier integral

The approximation is especially convenient when .

**[1]**H. WU & P. W. SCHMIDT, research to be published.**[2]**P. W. SCHMIDT,*J. Math. Phys.*, v. 7, 1966, p. 1295.**[3]**A. Erdélyi,*Asymptotic expansions*, Dover Publications, Inc., New York, 1956. MR**0078494****[4]**Norman Bleistein,*Uniform asymptotic expansions of integrals with stationary point near algebraic singularity*, Comm. Pure Appl. Math.**19**(1966), 353–370. MR**0204943****[5]**A. Erdélyi,*Asymptotic evaluation of integrals involving a fractional derivative*, SIAM J. Math. Anal.**5**(1974), 159–171. MR**0348360****[6]**W. MAGNUS & F. OBERHETTINGER,*Formulas and Theorems for the Functions of Mathematical Physics*, Chelsea, New York, 1954, p. 27.**[7]**F. W. J. Olver,*Asymptotics and special functions*, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Computer Science and Applied Mathematics. MR**0435697****[8]**Reference 6, p. 16, Equations (2a) and (2b).

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1978-0510821-9

Article copyright:
© Copyright 1978
American Mathematical Society