TWO CLASSES OF TWO DIMENSIONAL MIXED GEGENBAUER-LEGENDRE POLYNOMIALS TO APPLY IN COMPUTATION OF THE REGION OF CONVERGENCE OF ARBITRARY FUNCTION CONTAINING THEM

Abstract

In this article we introduce interesting two dimensional formulae of Legendre and Gegenbauer polynomials and then study their analytic and algebraic properties to derive some known and unknown results. Again we define two classes of two dimensional Gegenbauer-Legendre polynomials to obtain their series formulae. Finally, we use these results in the computation of the region of convergence of arbitrary function consisting of Gegenbauer-Legendre mixed polynomials.