On Sister Celine' s polynomials of several variables

Abstract

The aim of the present paper is to define Sister Celine's polynomials of two and more variables. We reduce the two variables Sister Celine's polynomials into many classical orthogonal polynomials and their product also such as - Jacobi, Gegenbauer, Legendre, Laguerre, Bessel and some discrete polynomials Bateman, Pasternak, Hahn, Krawtchouk, Meixner, Poisson-Charlier & others. Many integral representations and generating function relations are also established.