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Hsu, L. C.; Chou, Y. S.

An asymptotic formula for a type of singular oscillatory integrals. (English) Zbl 0527.41019

Math. Comput. 37, 503-507 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0527.41019

MSC:

41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
11J71 Distribution modulo one
11M35 Hurwitz and Lerch zeta functions

Keywords:

singular oscillatory integrals; Bernoulli polynomials
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References:

[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. · Zbl 0304.65016
[2] Tore Hȧvie, Remarks on an expansion for integrals of rapidly oscillating functions, Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 16 – 29. · Zbl 0273.65019
[3] L. C. Hsu, A refinement of the line integral approximation method and its application, Sci. Record (N.S.) 2 (1958), 193 – 196. · Zbl 0233.41011
[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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