Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Legendre-Gould Hopper Based Sheffer Polynomials: Properties and Applications

Version 1 : Received: 8 October 2020 / Approved: 9 October 2020 / Online: 9 October 2020 (13:04:41 CEST)

How to cite: Yasmin, G.; Muhyi, A. Legendre-Gould Hopper Based Sheffer Polynomials: Properties and Applications. Preprints 2020, 2020100204 (doi: 10.20944/preprints202010.0204.v1). Yasmin, G.; Muhyi, A. Legendre-Gould Hopper Based Sheffer Polynomials: Properties and Applications. Preprints 2020, 2020100204 (doi: 10.20944/preprints202010.0204.v1).

Abstract

In this article, the Legendre-Gould Hopper polynomials are combined with Sheffer sequences to introduce certain mixed type special polynomials. Generating functions, differential equations and certain other properties of Legendre-Gould Hopper based Sheffer polynomials are derived. Further, operational and integral representations providing connections between these polynomials and known special polynomials are established. Certain identities and results for some members of these new mixed polynomials are also obtained. Finally, the determinantal definitions of Legendre-Gould Hopper based Sheffer polynomials are also given.

Subject Areas

Legendre-Gould Hopper based Sheffer polynomials; Generating relations; Operational method; Monomiality principle; Determinantal definition

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