An asymptotic approximation for a type of Fourier integral
Paul W. Schmidt
Math. Comp. 32 (1978), 1171-1182
Primary 41A60; Secondary 42A76
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Abstract: A uniform asymptotic approximation which can be used for all is developed for the Fourier integral under the assumptions that , that the first derivatives of are continuous for , and that the first derivatives of are continuous at .
The approximation is especially convenient when .
H. WU & P. W. SCHMIDT, research to be published.
P. W. SCHMIDT, J. Math. Phys., v. 7, 1966, p. 1295.
Erdélyi, Asymptotic expansions, Dover Publications
Inc., New York, 1956. MR 0078494
Bleistein, Uniform asymptotic expansions of integrals with
stationary point near algebraic singularity, Comm. Pure Appl. Math.
19 (1966), 353–370. MR 0204943
Erdélyi, Asymptotic evaluation of integrals involving a
fractional derivative, SIAM J. Math. Anal. 5 (1974),
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W. MAGNUS & F. OBERHETTINGER, Formulas and Theorems for the Functions of Mathematical Physics, Chelsea, New York, 1954, p. 27.
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Reference 6, p. 16, Equations (2a) and (2b).
- H. WU & P. W. SCHMIDT, research to be published.
- P. W. SCHMIDT, J. Math. Phys., v. 7, 1966, p. 1295.
- A. ERDÉLYI, Asymptotic Expansions, Dover, New York, 1956, pp. 49-50. MR 0078494 (17:1202c)
- N. BLEISTEIN, Comm. Pure Appl. Math., v. 19, 1966, p. 353. MR 0204943 (34:4778)
- A. ERDÉLYI, SIAM J. Math. Anal., v. 5, 1974, p. 159. MR 0348360 (50:858)
- W. MAGNUS & F. OBERHETTINGER, Formulas and Theorems for the Functions of Mathematical Physics, Chelsea, New York, 1954, p. 27.
- F. W. J. OLVER, Asymptotics and Special Functions, Academic Press, New York, 1974, pp. 4-6. MR 0435697 (55:8655)
- Reference 6, p. 16, Equations (2a) and (2b).
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