ON A REDUCTION FORMULA FOR THE KAMP´ E de F´ ERIET FUNCTION
ON A REDUCTION FORMULA FOR THE KAMP´ E de F´ ERIET FUNCTION
The aim of this short research note is to provide a reduction formulafor the Kamp´e de F´eriet function Fh:2;0[-x, x] by employing a newg:2;0 summation formula for Clausen's series3F2[1] obtained recently by theauthors [Miskolc Math. Notes 10(2), 145-153, 2009.]
___
- [1] Appell, P. and Kamp´e de F´eriet, J. Fonctions hyperg´eom´etrique. Polyn^omes d'Hermite, (Gautier-Villars, Paris, 1926).
- [2] Bailey, W.N. Generalized Hypergeometric Series, Cambridge Tract, No. 32. (Cambridge University Press, Cambridge, 1935).
- [3] Burchnall, J.L. and Chaundy, T.W. Expansions of Appell's double hypergeometric functions, Quart. J. Math. (Oxford Ser.) 11, 249-270, 1940.
- [4] Buschmann R.G. and Srivastava, H.M. Some identities and reducibility of Kamp´e de F´eriet function, Math. Proc. Cambridge Philos. Soc. 91, 435-440, 1982.
- [5] Exton, H. On the reducibility of Kamp´e de F´eriet functions, J. Comput. Appl. Math. 83, 119-121, 1997.
- [6] Exton H. and Krupnikov, E.D. A register of computer-oriented reduction identities for the Kamp´e de F´eriet function. Draft manuscript. (Novosibirsk, Russia, 1998).
- [7] Karlsson, P.W. Some reduction formulae for power series and Kamp´e de F´eriet functions, Nederl. Akad. Wetensch. Indag. Math. 46(1), 31-36, 1984.
- [8] Kim,Y.-S., Pog´any, T.K. and Rathie, A.K. On a summation formula for the Clausen's series 3F2 with applications, Miskolc Math. Notes 10(2), 145-153, 2009.
- [9] Paris, R.B. A Kummer-type transformation for a 2F2 hypergeometric function, J. Comput. Appl. Math. 173, 379-382, 2005.
- [10] Rathie, A.K. and Paris, R.B. An extension of the Euler-type transformation for the 3F2 series, Far East J. Math. Sci.(FJMS) 27(1), 43-48, 2007.
- [11] Slater, L.J. Generalized Hypergeometric Functions, (Cambridge University Press, Cambridge, 1966).
- [12] Srivastava H.M. and Karlsson, P.W. Multiple Gaussian Hypergeometric Series, (Halsted Press (Ellis Norwood Limited, Chichester), John Wiley & Sons, New York, 1985).
- [13] Srivastava, H.M. and Manocha, H.L. A Treatise on Generating Functions, (Halsted Press (Ellis Norwood Limited, Chichester), John Wiley & Sons, New York, 1984).
- [14] Srivastava, H.M. and Panda, R. An integral representation for the product of two Jacobi polynomials, J. London Math. Soc. (2) 12, 419-425, 1976.