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Some expansion formulae for Fox's H-function involving exponential 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

In this paper we have evaluated some integrals involving Fox's Η-function and employed them to establish some expansion formulae for the Η-function involving exponential functions. Some results recently given by MacRobert (7) and Kesarwani (5) have been shown as particular cases.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1970

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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)Churchill, R. V.Fourier series and boundary value problems (McGraw-Hill; New York, 1941).Google Scholar
(3)Erdélyi, A.Higher transcendental functions, vol. 1 (McGraw-Hill; New York, 1953).Google Scholar
(4)Fox, C.The G and H-functions as symmetrical Fourier kernels. Trans. Amer. Math. Soc. 98 (1961), 395429.Google Scholar
(5)Kesarwani, R. N.Fourier series for Meijer's G-functions. Compositio Math. 17 (2) (1966), 149151.Google Scholar
(6)MacRobert, T. M.Functions of a complex variable (Macmillan; London, 1962).Google Scholar
(7)MacRobert, T. M.Fourier series for E-functions. Math. Z. 75 (1961), 7982.CrossRefGoogle Scholar