A Class of Multivariable Polynomials Associated with Humbert Polynomials

In this paper, we present a generalization (and unification) of a classof Humbert polynomials which include well known families of ChanChyan-Srivastava, Lagrange-Hermite and Erkus-Srivastava multivariable polynomials. We derive various families of multilateral and multilinear generating functions for these polynomials. We also obtain othermiscellaneous properties of these polynomials. Furthermore, for somespecial cases of these polynomials, we present hypergeometric representations and give expansions of these polynomials in series of someorthogonal polynomials.

Keywords:

Humbert polynomials, Chan-Chyan-Srivastava multivariable polynomials, Lagrange-Hermite multivariable polynomials, Erkus-Srivastava multivariable polynomials, Multilinear and multilateral generating function, Recurrence relation Hypergeometric function, 2000 AMS Classification: 33C45,

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