An asymptotic formula for a type of singular oscillatory integrals
Authors:
L. C. Hsu and Y. S. Chou
Journal:
Math. Comp. 37 (1981), 503-507
MSC:
Primary 41A60
DOI:
https://doi.org/10.1090/S0025-5718-1981-0628711-X
MathSciNet review:
628711
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Abstract | References | Similar Articles | Additional Information
Abstract: This paper offers a general expansion formula for oscillatory integrals of the form in which N is a large parameter, Nx denotes the fractional part of Nx, and
is a fixed real number in
. Our formula is expressed in terms of some ordinary integrals with integrands containing periodic Bernoulli functions and the generalized Riemann zeta function.
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- [2] T. Havie, "Remarks on an expansion for integrals of rapidly oscillating functions," BIT, v. 13, 1973, pp. 16-29. MR 0323077 (48:1435)
- [3] L. C. Hsu, "A refinement of the line integral approximation method and its application," Sci. Record (N. S. Academia Sinica), No. 6, 1958, pp. 193-196. MR 0101982 (21:784)
- [4] L. C. Hsu & Y. S. Chou, Numerical Integration in Higher Dimensions, Science Press, Peking, 1980, Chapter 14. (Chinese)
- [5] E. Riekstenš, "On asymptotic expansions of some integrals involving a large parameter," Učen. Zap. Leningrad. Gos. Univ., v. 41, 1961, pp. 5-23. (Russian)
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1981-0628711-X
Keywords:
Periodic Bernoulli function,
generalized Riemann zeta function,
Euler summation formula
Article copyright:
© Copyright 1981
American Mathematical Society