On a Class of Humbert-Hermite Polynomials

M.  A Pathan; Waseem Khan

doi:10.20944/preprints201909.0068.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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.

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

Computer Science and Mathematics, Mathematics

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On a Class of Humbert-Hermite Polynomials

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