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Online ISSN 1552-4485; Print ISSN 0033-569X
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
References | Similar Articles | Additional Information
-
N. Bleistein and R.A. Handelsman, Asymptotic expansion of integrals, Holt, Rinehart and Winston, New York, 1975
- G. B. Hagen, Über iterierte Integration von Bessel-Funktionen, Z. Angew. Math. Mech. 32 (1952), 27–30 (German). MR 46128, DOI https://doi.org/10.1002/zamm.19520320108
- 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), 405–433. 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), 31–37. 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), 56–58. MR 0035103
- Yudell L. Luke, Some notes on integrals involving Bessel functions, J. Math. Physics 29 (1950), 27–30. MR 0034908, DOI https://doi.org/10.1080/00031305.1950.10501658
- F. W. J. Olver, Error bounds for stationary phase approximations, SIAM J. Math. Anal. 5 (1974), 19–29. MR 333545, DOI https://doi.org/10.1137/0505003
- F. B. Pidduck, Lommel’s functions of small argument, Quart. J. Math. Oxford Ser. 17 (1946), 193–196. MR 19167, DOI https://doi.org/10.1093/qmath/os-17.1.193
- Paul W. Schmidt, Tables of $\int ^x_0 J_0(t)dt$ for large $x$, J. Math. and Phys. 34 (1955), 169–172. MR 71879, DOI https://doi.org/10.1002/sapm1955341169
- Kusum Soni, Classroom Notes: A Note on Asymptotic Expansions, Amer. Math. Monthly 85 (1978), no. 4, 268–269. MR 1538676, DOI https://doi.org/10.2307/2321172
- Kusum Soni, Exact error terms in the asymptotic expansion of a class of integral transforms. I. Oscillatory kernels, SIAM J. Math. Anal. 11 (1980), no. 5, 828–841. MR 586911, DOI https://doi.org/10.1137/0511074
- 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, 163–177. MR 603383, DOI https://doi.org/10.1016/0022-247X%2881%2990016-0
- E. C. Titchmarsh, The theory of functions, Oxford University Press, Oxford, 1958. Reprint of the second (1939) edition. MR 3155290 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 (1976), no. 6, 799–808. MR 415224, DOI https://doi.org/10.1137/0507061
- R. Wong, Error bounds for asymptotic expansions of integrals, SIAM Rev. 22 (1980), no. 4, 401–435. MR 593856, DOI https://doi.org/10.1137/1022086
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Article copyright:
© Copyright 1982
American Mathematical Society