PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 62 (76), pp. 53--62 (1997)
On polynomials associated with Humbert's polynomials}
M.A. Pathan and M.A. KhanDepartment of Mathematics, Aligarh Muslim University, Aligarh, India
Abstract: The principal object of this paper is to provide a natural further step toward the unified presentation of a class of Humbert's polynomials which generalizes the well known class of Gegenbauer, Legendre, Pincherle, Horadam, Kinney, Horadam-Pethe, Gould and Milovanovi\'c-Djordjevi\'c polynomials and many not so well-known polynomials. We shall give some basic relations involving the generalized Humbert polynomials and then take up several generating functions, hypergeometric representations and expansions in series of some relatively more familiar polynomials of Legendre, Gegenbauer, Hermite and Laguerre. Some of these results may be looked upon as providing useful extensions of the known results of Dilcher, Horadam, Sinha, Shreshtha and Milovanovi\'c-Djordjevi\'c.
Keywords: Humbert's polynomials, Gegenbauer polynomials, Horadam polynomials, Kinney polynomials, Pincherle polynomials and Horadam-Pethe polynomials.
Classification (MSC2000): 33C35
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