Some Generating Functions for a Class of Hypergeometric Polynomials

Yıl 2018, Cilt: 31 Sayı: 4, 1179 - 1190, 01.12.2018

Nejla Ozmen Esra Erkus Duman

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• [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).