Asymptotic expansion of the Hankel transform with explicit remainder terms
Author:
K. Soni
Journal:
Quart. Appl. Math. 40 (1982), 1-14
MSC:
Primary 41A60; Secondary 44A15
DOI:
https://doi.org/10.1090/qam/652045
MathSciNet review:
652045
Full-text PDF Free Access
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N. Bleistein and R.A. Handelsman, Asymptotic expansion of integrals, Holt, Rinehart and Winston, New York, 1975
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- Richard A. Handelsman and John S. Lew, Asymptotic expansion of a class of integral transforms with algebraically dominated kernels, J. Math. Anal. Appl. 35 (1971), 405β433. MR 278012, DOI https://doi.org/10.1016/0022-247X%2871%2990227-7
- C. W. Horton, On the extension of some Lommel integrals to Struve functions with an application to acoustic radiation, J. Math. Physics 29 (1950), 31β37. MR 0034907
- C. W. Horton, A short table of Struve functions and of some integrals involving Bessel and Struve functions, J. Math. Physics 29 (1950), 56β58. MR 0035103
- Yudell L. Luke, Some notes on integrals involving Bessel functions, J. Math. Physics 29 (1950), 27β30. MR 0034908, DOI https://doi.org/10.1080/00031305.1950.10501658
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- K. Soni and R. P. Soni, A note on uniform asymptotic expansions of finite $K_{\nu }$ and related transforms with explicit remainder, J. Math. Anal. Appl. 79 (1981), no. 1, 163β177. MR 603383, DOI https://doi.org/10.1016/0022-247X%2881%2990016-0
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E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford, London, 1959
G. N. Watson, Theory of Bessel functions, Cambridge, London, 1958
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N. Bleistein and R.A. Handelsman, Asymptotic expansion of integrals, Holt, Rinehart and Winston, New York, 1975
G. B. Hagen, Uber iterierte Integration von Bessel-Funktionen, Z. Angew. Math. Mech. 32, 27β30 (1952)
R. A. Handelsman and J. S. Lew, Asymptotic expansion of a class of integral transforms with algebraically dominated kernels, J. Math. Anal. Appl. 35, 405β433 (1971)
C. W. Horton, On the extension of some Lommel integrals to Struve functions with an application to acoustic radiation, J. Math. Phys., 29, 31β37 (1950)
C. W. Horton, A short table of Struve functions and some integrals involving Bessel and Struve functions, J. Math. Phys. 29, 56β58 (1950)
Y. L. Luke, Some notes on integrals involving Bessel functions, J. Math. Phys. 29, 27β30 (1950)
F. W. J. Olver, Error bounds for stationary phase approximation, SIAM J. Math. Anal. 5, 19β29 (1974)
F. B. Pidduck, Lommelβs functions of small argument, Quart. J. Math., Oxford Ser. 17, 193β196 (1946)
P. W. Schmidt, Tables of $\smallint _0^x{J_0}(t)dt$ dt for large x, J. Math. Phys. 34, 169β172 (1955)
K. Soni, A note on asymptotic expansions, Am. Math. Monthly 85, 268β269 (1978)
K. Soni, Exact error terms in the asymptotic expansion of a class of integral transforms I, SIAM J. Math. Anal. 11, 828β841 (1980)
K. Soni and R. P. Soni, A note on uniform asymptotic expansions of finite K$_{v}$ and related transforms with explicit remainder, J. Math. Anal. Appl. 79, 163β177 (1981)
E. C. Titchmarsh, Theory of functions, Oxford, London, 1958
E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford, London, 1959
G. N. Watson, Theory of Bessel functions, Cambridge, London, 1958
R. Wong, Error bounds for asymptotic expansions of Hankel transforms, SIAM J. Math. Anal. 7, 799β808 (1976)
R. Wong, Error bounds for asymptotic expansions of integrals, SIAM Review 22, 401β435 (1976)
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© Copyright 1982
American Mathematical Society