Applications of Some Hypergeometric Summation Theorems Involving Double Series

[1] P. Appell and J. Kampé de Fériet, Fonctions Hypergéométriques et Hypersphériques; Polyn^omes d'Hermite, Gauthier-Villars, Paris, 1926.Search in Google Scholar

[2] R. G. Buschman and H. M. Srivastava, Series identities and reducibility of Kampé de Fériet functions, Math. Proc. Cambridge Philos. Soc. 91 (1982), 435-440.10.1017/S0305004100059478Search in Google Scholar

[3] K.-Y. Chen and H. M. Srivastava, Series identities and associated families of generating functions, J. Math. Anal. Appl. 311 (2005), 582-599.10.1016/j.jmaa.2005.03.030Search in Google Scholar

[4] K.-Y. Chen, S.-J. Liu and H. M. Srivastava, Some double-series identities and associated generating-function relationships, Appl. Math. Lett. 19 (2006), 887-893.10.1016/j.aml.2005.07.013Search in Google Scholar

[5] H. Exton, Multiple Hypergeometric Functions and Applications, Halsted Press (Ellis Hor- wood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1976.Search in Google Scholar

[6] N. T. H ; ai, H. M. Srivastava and O. I. Marichev, A note on the convergence of certain families of multiple hypergeometric series, J. Math. Anal. Appl. 164 (1992), 104-115.10.1016/0022-247X(92)90147-6Search in Google Scholar

[7] A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, Integrals and Series, Vol. 3: More Special Functions, Nauka, Moscow, 1986 (In Russian); Translated from the Russian by G. G. Gould, Gordon and Breach Science Publishers, New York, Philadelphia, London, Paris, Montreux, Tokyo and Melbourne, 1990.Search in Google Scholar

[8] M. I. Qureshi, K. A. Quraishi and H. M. Srivastava, Some hypergeometric summation formulas and series identities associated with exponential and trigonometric functions, Integral Transforms Spec. Funct. 19 (2008), 267-276.10.1080/10652460801896024Search in Google Scholar

[9] E. D. Rainville, Special Functions, Macmillan Company, New York, 1960: Reprinted by Chelsea Publication Company, Bronx, New York, 1971.Search in Google Scholar

[10] L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cam- bridge, London and New York, 1966.Search in Google Scholar

[11] H. M. Srivastava and M. C. Daoust, On Eulerian integrals associated with Kampé de Fériet's function, Publ. Inst. Math. (Beograd) (N. S.) 9 (23) (1969), 199-202.Search in Google Scholar

[12] H. M. Srivastava and M. C. Daoust, Certain generalized Neumann expansions associated with the Kampé de Fériet function, Nedrel. Akad. Wetensch. Proc. Ser. A 72 = Indag.Math. 31 (1969), 449-457.Search in Google Scholar

[13] H. M. Srivastava and M. C. Daoust, A note on the convergence of Kampé de Fériet's double hypergeometric series, Math. Nachr. 53 (1972), 151-157.10.1002/mana.19720530114Search in Google Scholar

[14] H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Bris- bane and Toronto, 1985.Search in Google Scholar

[15] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984.Search in Google Scholar