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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


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
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 $ \smallint _0^1{x^{ - \alpha }}f(x,\{ Nx\} )\,dx$ in which N is a large parameter, Nx denotes the fractional part of Nx, and $ \alpha $ is a fixed real number in $ 0 < \alpha < 1$. Our formula is expressed in terms of some ordinary integrals with integrands containing periodic Bernoulli functions and the generalized Riemann zeta function.

References [Enhancements On Off] (What's this?)

  • [1] Philip J. Davis and Philip Rabinowitz, Methods of numerical integration, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers]\ New York-London, 1975. Computer Science and Applied Mathematics. MR 0448814 (56 #7119)
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Additional Information

PII: S 0025-5718(1981)0628711-X
Keywords: Periodic Bernoulli function, generalized Riemann zeta function, Euler summation formula
Article copyright: © Copyright 1981 American Mathematical Society

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