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Series identities and reducibility of Kampé de Fériet functions

  • R. G. Buschman (a1) and H. M. Srivastava (a2)
Extract

The work of H. M. Srivastava (9) on generalizations of an interesting identity of Carlson is expanded upon in order to obtain series identities analogous to all four of the Appell functions and their generalizations. Reduction formulas for some Kampé de Fériet functions are derived as consequences of the various double-series identities considered in this paper.

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COPYRIGHT: © Cambridge Philosophical Society 1982
References
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(1)Appell, P. et Kampé De Fébiet, J.Fonctions hypergéométriques et hyperspériques: Polynômes d'Hermite (Gauthier-Villars, Paris, 1926).
(2)Bailey, W. N.On the sum of a terminating 3F 2(1). Quart. J. Math. Oxford Ser. (2) 4 (1953), 237–240.
(3)Burchnall, J. L. and Chaundy, T. W.Expansions of Appell's double hypergeometric functions. Quart. J. Math. Oxford Ser. 11 (1940), 249–270.
(4)ErdÉlyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher transcendental functions, vol. I (McGraw-Hill, New York, Toronto and London, 1953).
(5)Exton, H.Multiple hypergeometric functions and applications. (Halsted Press, John Wiley, New York, London, Sydney and Toronto, 1976).
(6)Panda, R.Some multiple series transformations. Jñãnabha Sect. A 4 (1974), 165–168.
(7)Srivastava, H. M.On the reducibility of Appell's function F 4, Canad. Math. Bull. 16 (1973), 295–298.
(8)Srivastava, H. M.A note on certain summation theorems for multiple hypergeometric series. Simon Stevin 52 (1978), 97–109.
(9)Srivastava, H. M.Some generalizations of Carlson's identity. Boll. Un. Mat. Ital. (5) 18 A (1981), 138–143.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
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