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An infinite summation formula associated with Appell's function F2

Published online by Cambridge University Press:  24 October 2008

H. M. Srivastava
H. M. Srivastava
Affiliation:
Department of Mathematics, West Virginia University, Morgantown, West Virginia, U.S.A.
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Extract

1. Recently in these proceedings we proved that, if ℜ(α) > 1 and ℜ(α) > − 1, then ((10), p. 1088)

where F2 denotes the Appell function (see, e.g., (8), p. 211),

with, as usual,

and for covergence of the double series,

and x⇌y indicates the presence of a second term that originates from the first by interchanging x and y.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 3 , May 1969 , pp. 679 - 682
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Appell, P.et Kampé de Fériet, J.Fonctions hypergéométriques et hypersphériques (Paris: Gauthier–Villars, 1926).Google Scholar
(2)Bailey, W. N.Generalized hypergeometric series (Cambridge, 1935).Google Scholar
(3)Erdélyi, A.Transformations of hypergeometric functions of two variables. Proc. Roy. Soc. Edinburgh, Sect. A 62 (1948), 378–385.Google Scholar
(4)Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher transcendental functions, vol. I (New York: McGraw-Hill, 1953).Google Scholar
(5)Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher transcendental functions, vol. II (New York: McGraw-Hill, 1953).Google Scholar
(6)Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Tables of integral transforms, vol. II (New York: McGraw-Hill, 1954).Google Scholar
(7)Slater, L. J.Confluent hypergeometric functions (Cambridge, 1960).Google Scholar
(8)Slater, L. J.Generalized hypergeometric functions (Cambridge, 1966).Google Scholar
(9)Srivastava, H. M.The integration of generalized hypergeometric functions. Proc. Cambridge Philos. Soc. 62 (1966), 761–764.CrossRefGoogle Scholar
(10)Srivastava, H. M.On a summation formula for the Appell function F2. Proc. Cambridge Philos. Soc. 63 (1967), 1087–1089.CrossRefGoogle Scholar