CERTAIN GENERATING FUNCTIONS OF GENERALIZED HYPERGEOMETRIC 2D POLYNOMIALS FROM TRUESDELL’S METHOD

Abstract

In this paper, the generating functions for generalized Hypergeometric 2D polynomials U_n (β, γ, x, y) are obtained by using the Truesdell’s method giving a suitable interpretation to the index n.  Further, a pair of linearly independent differential recurrence relations are used in order to derive generating functions for U_n (β, γ, x, y).  The principal interest in our results lies in the fact that, how the Truesdell’s method is utilized in an effective and suitable way to generalized Hypergeometric 2D polynomials in order to derive two generating functions independently from ascending and descending recurrence relations respectively.