Some Generating Functions for a Class of Hypergeometric Polynomials

The present study deals with some new properties for the hypergeometric polynomials . The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties and also some special cases for these polynomials. In addition, we derive a theorem giving certain families of bilateral generating functions for the hypergeometric polynomials and the generalized Lauricella functions. Finally, we get several interesting results of this theorem.

Keywords:

Hypergeometric polynomials, Generating function Multilinear and multilateral generating function, Recurrence relation,

PDF

___

[6] Lauricella, G., Sulle funzioni ipergeometriche a più variabili, Rend. Circ. Mat. Palermo 7, 111-158, (1893).
[7] Exton, H. , Multiple Hypergeometric Functions and Applicaions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, (1976).
[8] Qureshi, M.I. , Khan, M.S. and Pathan, M.A. , Some multiple Gaussian hypergeometric generalizations of Buschman--Srivastava theorem, Internal J. Math. Math. Sci. 2005, 143-153, (2005).
[9] Srivastava, H.M. and Karlsson, P.W. , Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, (1985).
[10] Özmen, N. and Erkuş-Duman, E., On the Poisson-Charlier polynomials, Serdica Math. J. 41. 457-470, (2015).
[11] Özmen, N. and Erkuş-Duman, E., Some families of generating functions for the generalized Cesáro polynomials, J. Comput. Anal. Appl. (accepted for publication).
[7] Exton, H. , Multiple Hypergeometric Functions and Applicaions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, (1976).
[8] Qureshi, M.I. , Khan, M.S. and Pathan, M.A. , Some multiple Gaussian hypergeometric generalizations of Buschman--Srivastava theorem, Internal J. Math. Math. Sci. 2005, 143-153, (2005).
[9] Srivastava, H.M. and Karlsson, P.W. , Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, (1985).
[10] Özmen, N. and Erkuş-Duman, E., On the Poisson-Charlier polynomials, Serdica Math. J. 41. 457-470, (2015).
[11] Özmen, N. and Erkuş-Duman, E., Some families of generating functions for the generalized Cesáro polynomials, J. Comput. Anal. Appl. (accepted for publication).