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Some finite integrals involving F4 and H-functions

Published online by Cambridge University Press:  24 October 2008

P. N. Rathie
P. N. Rathie
Affiliation:
M. R. Engineering College, Jaipur, India
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Extract

1. The object of the present paper is to obtain some finite integrals involving the Appell's function F4 and the H-function of Fox by utilizing the results recently given by Saxena, Sharma and Tranter respectively. The first three results proved in this paper are the extension of the results recently established by Saxena and Sharma in these proceedings. MacRobert's result follows as a very special case of one of our results. A few very interesting special cases of the main results have also been given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 1077 - 1081
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Bailey, W. N.Some infinite integrals involving Bessel functions. Proc. London Math. Soc. 40 (1935), 37–48.Google Scholar
(2)Bromwich, T. J. I'A.An introduction to the theory of infinite series (Macmillan; London, 1931).Google Scholar
(3)Burchnall, J. L.Differential equations associated with hypergeometric functions. Quart. J. Math. Oxford 13 (1942), 90–106.CrossRefGoogle Scholar
(4)Fox, C.The G and H functions as symmetrical Fourier kernels. Trans. Amer. Math. Soc. 98 (1961), 395–429.Google Scholar
(5)Gupta, K. C.On the H-function, Ann. Soc. Sci. Bruxelles, Ser. I 79 (1965), 97–106.Google Scholar
(6)MacRobert, T. M.Some formulae for the associated Legendre functions of the first kind. Philos. Mag. 27 (1939), 703–705.CrossRefGoogle Scholar
(7)Saxena, R. K.A definite integral involving associated Legendre function of the first kind. Proc. Cambridge Philos. Soc. 57 (1961), 281–283.CrossRefGoogle Scholar
(8)Sharma, K. C.Theorems relating Hankel and Meijer's Bessel transforms. Proc. Glasgow Math. Assoc. 6 (1963), 107–112.CrossRefGoogle Scholar
(9)Sharma, K. C.Integrals involving products of G-function and Gauss's hypergeometric function. Proc. Cambridge Philos. Soc. 60 (1964), 539–542.CrossRefGoogle Scholar
(10)Tranter, C. J.A generalization of Sonine's first finite integral. Proc. Glasgow Math. Assoc. 6 (1963), 97–98.CrossRefGoogle Scholar