A certain class of generating functions involving bilateral series

Srivástava, H. M.; Pathan, M. A.; Bin-Saad, Maged G.

doi:10.1017/s1446181100008154

Cited by 5 publications

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References 6 publications

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“…Furthermore, we recall here an interesting (partly bilateral and partly unilateral) generating function for L (α) n (x) due to Exton [9] in the following modified form (see Pathan and Yasmeen [19], Pathan and Bin-Saad [22]):…”

Section: Introductionmentioning

confidence: 99%

A New Class of Laguerre-Based Generalized Hermite-Euler Polynomials and its Properties

Khan¹,

Usman²,

Khan³

2020

KgJMat

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The special polynomials of more than one variable provide new means of analysis for the solutions of a wide class of partial differential equations often encountered in physical problems. Motivated by their importance and potential for applications in a variety of research fields, recently, numerous polynomials and their extensions have been introduced and investigated. In this paper, we introduce a new family of Laguerre-based generalized Hermite-Euler polynomials, which are related to the Hermite, Laguerre and Euler polynomials and numbers. The results presented in this paper are based upon the theory of the generating functions. We derive summation formulas and related bilateral series associated with the newly introduced generating function. We also point out that the results presented here, being very general, can be specialized to give many known and new identities and formulas involving relatively simple numbers and polynomials.

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Section: Introductionmentioning

confidence: 99%