References
- P. Appell and J. Kampe de Feriet, Fonctions Hypergeometriques et Hyper-spheriques; Polynomes d'Hermite, Gauthier-Villars, Paris, 1926.
- W. N. Bailey, Product of generalized hypergeometric series, Proc. London Math. Soc. (ser. 2) 28 (1928), 242-254.
- W. N. Bailey, Generalized Hypergeometric Series, Stechert Hafner, New York, 1964.
- J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeomet-ric functions, Quart. J. Math. (Oxford ser.) 11 (1940), 249-270.
- J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeomet-ric functions (II), Quart. J. Math. (Oxford ser.) 12 (1941), 112-128.
- R. G. Buschman and H. M. Srivastava, Some identities and reducibility of Kampe de Feriet functions, Math. Proc. Cambridge Philos. Soc. 91 (1982), 435-440. https://doi.org/10.1017/S0305004100059478
- H. Exton, Multiple hypergeometric functions, Ellis Horwood, Chichester, UK, 1976.
- H. Exton, On the reducibility of the Kampe de Feriet function, J. Comput. Appl. Math. 83 (1997), 119-121. https://doi.org/10.1016/S0377-0427(97)86597-1
- P. W. Karlsson, Some reduction formulae for power series and Kampe de Feriet function, Proc. A. Kon, Nederl. Akad. Weten. 87 (1984), 31-36. https://doi.org/10.1016/1385-7258(84)90053-2
- Y. S. Kim, On certain reducibility of Kampe de Feriet function, Honam Math. J. 31(2) (2009), 167-176. https://doi.org/10.5831/HMJ.2009.31.2.167
- Y. S. Kim, M. A. Rakha, and A. K. Rathie, Generalization of Kummer's second theorem with applications, Comput. Math. Math. Phys. 50(3) (2010), 387-402. https://doi.org/10.1134/S0965542510030024
-
Y. S. Kim, M. A. Rakha, and A. K. Rathie, Extensions of certain classical summation theorems for the series
$_2F_1$ and$_3F_2$ with applications in Ramanujan's summations, Int. J. Math. Math. Sci. 2010, to appear. - E. D. Krupnikon, A Register of Computer-Oriented Reduction Identities for the Kampe de Feriet function, Novosibirsk, Russia, 1996.
-
J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizations of Watson's theorem on the sum of a
$_3F_2$ , Indian J. Math. 34(2) (1992), 23-32. -
J. L. Lavoie, F. Grondin, A. K. Rathie, and K. Arora, Generalizations of Dixon's theorem on the sum of a
$_3F_2$ , Math. Comput. 62 (1994), 267-276. -
J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizations of Whipple's theorem on the sum of a
$_3F_2$ , J. Comput. Appl. Math. 72 (1996), 293-300. https://doi.org/10.1016/0377-0427(95)00279-0 -
S. Lewanowicz, Generalized Watson's summation formula for
$_3F_2$ (1), J. Comput. Appl. Math. 86 (1997), 375-386. https://doi.org/10.1016/S0377-0427(97)00170-2 -
M. Milgram, On hypergeometric
$_3F_2(1)$ , Arxiv: math. CA/ 0603096, 2006. - E. D. Rainville, Special Functions, Macmillan Company, New York, 1960;Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
-
M. A. Rakha and A. K. Rathie, Generalizations of classical summation theorems for the series
$_2F_1$ and$_3F_2$ with applications, submitted for publication, 2010. - A. K. Rathie and J. Choi, Another proof of Kummer's second theorem, Commun. Korean Math. Soc. 13 (1998), 933-936.
- A. K. Rathie and V. Nagar, On Kummer's second theorem involving product of generalized hypergeometric series, Le Math. (Catania) 50 (1995), 35-38.
- L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, London, and New York, 1966.
- H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.
- H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane, and Toronto, 1985.
- 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.
- H. M. Srivastava and R. Panda, An integral representation for the product of two Jacobi polynomials, J. London Math. Soc. 12(2) (1976), 419-425.
- R. Vidunas, A generalization of Kummer's identity, Rocky Mount. J. Math. 32 (2002), 919-935; also available at http://arxiv.org/abs/mathCA/005095. https://doi.org/10.1216/rmjm/1030539701
Cited by
- On a reducibility of the Kampé de Fériet function vol.38, pp.12, 2015, https://doi.org/10.1002/mma.3245