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Fourier series of generalized hypergeometric functions

Published online by Cambridge University Press:  24 October 2008

S. D. Bajpai
Affiliation:
Department of Mathematics, Shri G. S. Technological Institute, Indore (India)

Extract

1. The object of this paper is to evaluate two integrals involving Fox's H-function and employ them to establish two Fourier series for the H-function. Some Fourier series for Meijer's G-function and MacRobert's E-function are obtained as particular cases. Some results recently given by MacRobert(6, 7), Jain (4) and Kesarwani(5) are shown as particular cases.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Braaksma, B. L. J.Asymptotic expansions and analytic continuations for a class of Barnes integrals. Compositio Math. 15 (1963), 239341.Google Scholar
(2)Ebdélyi, A.Higher transcendental functions, vol. 1 (New York: McGraw-Hill, 1953.)Google Scholar
(3)Fox, C.The G and H-functions as symmetrical Fourier kernels. Trans. Amer. Math. Soc. 98 (1961), 395429.Google Scholar
(4)Jain, R. N.Some infinite series of G-functions. Math. Japon. 10 (1965), 101105.Google Scholar
(5)Kesarwani, R. N.Fourier series for Meijer's G-function. Compositio Math. 17 (2), (1966), 149151.Google Scholar
(6)MacRobebt, T. M.Infinite series of E-functions. Math. Z. 71 (1959), 143145.CrossRefGoogle Scholar
(7)MacRobebt, T. M.Fourier series for E-functions. Math. Z. 75 (1961), 7982.CrossRefGoogle Scholar