Generalized Gould-Hopper Polynomials

Year 2021, Volume: 9 Issue: 1, 102 - 111, 28.04.2021

Nejla Özmen Mustafa Topaloğlu

Abstract

In this paper, we derive generating functions for the generalized Gould-Hopper polynomials in terms of the generalized Lauricella function by using series rearrangement techniques. Further, we derive the summation formulae for that polynomials by using different analytical means on its generating function or by using certain operational techniques. Also, generating functions and summation formulae for the polynomials related to generalized Gould-Hopper polynomials are obtained as applications of main results. In addition, we derive a theorem giving certain families of bilateral generating functions for the generalized Gould-Hopper polynomials. The results obtained here include various families of bilinear and bilateral generating functions, miscellaneous properties and also some special cases for these polynomials.

Keywords

Generalized Gould-Hopper polynomials, Lauricella functions, summation formulae, generating function

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