Some expansions in series of Bessel functions
Authors:
H. M. Srivastava and R. M. Shreshtha
Journal:
Quart. Appl. Math. 46 (1988), 451-458
MSC:
Primary 33A35; Secondary 41A58
DOI:
https://doi.org/10.1090/qam/963581
MathSciNet review:
963581
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Abstract: A general theorem on generating functions is applied to derive a number of interesting expansions for the generalized hypergeometric $_r{F_s}$ function in series of Bessel functions. Several further expansion formulas, relevant to the present discussion, are also considered. Many of these expansions in series of Bessel functions stem from (or are motivated by) their applicability in various seemingly diverse fields of applied sciences and engineering. With this point in view, some examples illustrating possible applications of these results are provided.
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A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, Vol. II, McGraw-Hill, New York, Toronto and London, 1953
Y. L. Luke, Integrals of Bessel Functions, McGraw-Hill, New York, Toronto and London, 1962
Y. L. Luke, The Special Functions and Their Approximations, Vol. II, Academic Press, New York and London, 1969
Y. L. Luke, Mathematical Functions and Their Approximations, Academic Press, New York, San Francisco and London, 1975
R. M. Shreshtha, Expansions in series of Bessel functions, C. R. Acad. Bulgare Sci. 35, 295–297 (1982)
H. M. Srivastava, Some expansions of generalized Whittaker functions, Proc. Cambridge Philos. Soc. 61, 895–896 (1965)
H. M. Srivastava, Some polynomial expansions for functions of several variables, IMA J. Appl. Math. 27, 299–306 (1981)
H. M. Srivastava and M. C. Daoust, Certain generalized Neumann expansions associated with the Kampé de Fériet function, Nederl. Akad. Wetensch. Indag. Math. 31, 449–457 (1969)
H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985
H. M. Srivastava and R. Panda, Expansion theorems for the H function of several complex variables, J. Reine Angew. Math. 288, 129–145 (1976)
H. M. Srivastava and R. Panda, A note on certain results involving a general class of polynomials, Boll. Un. Mat. Ital. A (5) 16, 467–474 (1979)
G. N. Watson, A Treatise on the Theory of Bessel Functions, Second ed., Cambridge University Press, Cambridge, London and New York, 1966
A. Yariv, An Introduction to Theory and Applications of Quantum Mechanics, John Wiley and Sons, New York, Chichester, Brisbane, Toronto and Singapore, 1982
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Article copyright:
© Copyright 1988
American Mathematical Society
