Asymptotic expansions of integrals of certain rapidly oscillating functions

Authors:
U. Banerjee, L. J. Lardy and A. Lutoborski

Journal:
Math. Comp. **49** (1987), 243-249

MSC:
Primary 41A55; Secondary 41A60

DOI:
https://doi.org/10.1090/S0025-5718-1987-0890265-6

MathSciNet review:
890265

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Abstract: An expansion in terms of powers of is given for integrals of the form , where *m* is a positive integer, is an integrable rapidly oscillating function with period , and is a smooth function.

**[1]**M. Abramowitz & I. A. Stegun,*Handbook of Mathematical Functions*, Dover, New York, 1972.**[2]**A. Bensoussan, J. L. Lions & G. Papanicolaou,*Asymptotic Analysis for Periodic Structures*, North-Holland, Amsterdam, 1978. MR**503330 (82h:35001)****[3]**P. J. Davis,*Interpolation and Approximation*, Dover, New York, 1975. MR**0380189 (52:1089)****[4]**V. I. Krylov,*Approximate Calculation of Integrals*, Macmillan, New York, 1962. MR**0144464 (26:2008)****[5]**J. N. Lyness, "The calculation of Fourier coefficients by the Möbius inversion of the Poisson summation formula, Part I. Functions whose early derivatives are continuous,"*Math. Comp.*, v. 24, 1970, pp. 101-135. MR**0260230 (41:4858)****[6]**H. J. Stetter, "Numerical approximation of Fourier transforms,"*Numer. Math.*, v. 8, 1966, pp. 235-249. MR**0198716 (33:6870)**

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DOI:
https://doi.org/10.1090/S0025-5718-1987-0890265-6

Article copyright:
© Copyright 1987
American Mathematical Society