Preprint Article Version 1 This version is not peer-reviewed

On a Class of Humbert-Hermite Polynomials

Version 1 : Received: 5 September 2019 / Approved: 6 September 2019 / Online: 6 September 2019 (04:02:50 CEST)

How to cite: Pathan, M..A.; Khan, W. On a Class of Humbert-Hermite Polynomials. Preprints 2019, 2019090068 (doi: 10.20944/preprints201909.0068.v1). Pathan, M..A.; Khan, W. On a Class of Humbert-Hermite Polynomials. Preprints 2019, 2019090068 (doi: 10.20944/preprints201909.0068.v1).

Abstract

A unified presentation of a class of Humbert’s polynomials in two variables which generalizes the well known class of Gegenbauer, Humbert, Legendre, Chebycheff, Pincherle, Horadam, Kinnsy, Horadam-Pethe, Djordjević , Gould, Milovanović and Djordjević, Pathan and Khan polynomials and many not so called ’named’ polynomials has inspired the present paper and the authors define here generalized Humbert-Hermite polynomials of two variables. Several expansions of Humbert- Hermite polynomials, Hermite-Gegenbaurer (or ultraspherical) polynomials and Hermite- Chebyshev polynomials are proved.

Subject Areas

Hermite polynomials; Humbert polynomials; Gegenbauer polynomials; Chebyshev polynomials; Pathan-Khan polynomials; hypergeometric function

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