Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


An asymptotic formula for a type of singular oscillatory integrals
HTML articles powered by AMS MathViewer

by L. C. Hsu and Y. S. Chou PDF
Math. Comp. 37 (1981), 503-507 Request permission


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.
  • Philip J. Davis and Philip Rabinowitz, Methods of numerical integration, Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0448814
  • Tore Hȧvie, Remarks on an expansion for integrals of rapidly oscillating functions, Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 16–29. MR 323077, DOI 10.1007/bf01933520
  • L. C. Hsu, A refinement of the line integral approximation method and its application, Sci. Record (N.S.) 2 (1958), 193–196. MR 101982
  • L. C. Hsu & Y. S. Chou, Numerical Integration in Higher Dimensions, Science Press, Peking, 1980, Chapter 14. (Chinese) E. Riekstenš, "On asymptotic expansions of some integrals involving a large parameter," Učen. Zap. Leningrad. Gos. Univ., v. 41, 1961, pp. 5-23. (Russian)
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 41A60
  • Retrieve articles in all journals with MSC: 41A60
Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 503-507
  • MSC: Primary 41A60
  • DOI:
  • MathSciNet review: 628711