An asymptotic approximation for a type of Fourier integral
Author:
Paul W. Schmidt
Journal:
Math. Comp. 32 (1978), 11711182
MSC:
Primary 41A60; Secondary 42A76
MathSciNet review:
0510821
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Abstract 
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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 .
 [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
(17,1202c)
 [4]
Norman
Bleistein, Uniform asymptotic expansions of integrals with
stationary point near algebraic singularity, Comm. Pure Appl. Math.
19 (1966), 353–370. MR 0204943
(34 #4778)
 [5]
A.
Erdélyi, Asymptotic evaluation of integrals involving a
fractional derivative, SIAM J. Math. Anal. 5 (1974),
159–171. MR 0348360
(50 #858)
 [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 YorkLondon,
1974. Computer Science and Applied Mathematics. MR 0435697
(55 #8655)
 [8]
Reference 6, p. 16, Equations (2a) and (2b).
 [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, New York, 1956, pp. 4950. MR 0078494 (17:1202c)
 [4]
 N. BLEISTEIN, Comm. Pure Appl. Math., v. 19, 1966, p. 353. MR 0204943 (34:4778)
 [5]
 A. ERDÉLYI, SIAM J. Math. Anal., v. 5, 1974, p. 159. MR 0348360 (50:858)
 [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, New York, 1974, pp. 46. MR 0435697 (55:8655)
 [8]
 Reference 6, p. 16, Equations (2a) and (2b).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197805108219
PII:
S 00255718(1978)05108219
Article copyright:
© Copyright 1978
American Mathematical Society
