On polynomials associated with Humbert's polynomials}

M.A. Pathan and M.A. Khan

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

Full text of the article:

• Compressed PostScript file (59 kilobytes)
• PDF file (152 kilobytes)