Some Results on the Bivariate Laguerre Polynomials

Abstract

In this paper, we consider the general class of bivariate Laguerre polynomials introduced in Ozarslan and Krt (On a double integral equation including a set of two variables polynomials suggested by Laguerre polynomials. In: Proceedings of international conference on recent advances in pure and applied mathematics (ICRAPAM2014), 2014). We first obtain linear and mixed multilateral generating functions for the above-mentioned classes. We further derive a finite summation formula for our polynomials: Finally, by using the fractional derivative operator, we give a series relation between the bivariate Laguerre polynomials and a product of confluent hypergeometric functions.