Operational evaluation of certain infinite Bessel function integrals

Authors:
Stanley E. Babb and James W. Cafky

Journal:
Math. Comp. **33** (1979), 1033-1039

MSC:
Primary 44A99

DOI:
https://doi.org/10.1090/S0025-5718-1979-0528055-1

MathSciNet review:
528055

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Abstract: Some infinite integrals, primarily over trigonometric functions, are operationally evaluated by two extensions of the Weber-Schafheitlin approach.

**[1]**J. W. CAFKY, Ph. D. dissertation, University of Oklahoma, 1969.**[2]**W. N. BAILEY, "Some infinite integrals involving Bessel functions,"*Proc. London Math. Soc.*(2), v. 40, 1936, pp. 37-48, Eq. 10.3. Also G. N. WATSON,*A Treatise on the Theory of Bessel Functions*, Cambridge Univ. Press, 1966, p. 419 (16).**[3]**G. N. WATSON,*ibid.*, p. 404.**[4]**G. N. WATSON,*ibid.*, p. 399 ff.**[5]**S. KATSURA,*Phys. Rev.*, v. 115, 1959, p. 1417; S. KATSURA & K. NISHIHARA,*J. Chem. Phys.*, v. 50, 1969, p. 3579; J. E. KILPATRICK, S. KATSURA & Y. INOUE,*Math. Comp.*, v. 21, 1967, pp. 267 and 407. MR**0108015 (21:6736)**

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0528055-1

Keywords:
Fourier transforms,
Bessel functions

Article copyright:
© Copyright 1979
American Mathematical Society