New mixed recurrence relations of two-variable orthogonal polynomials via differential operators

Abstract

In this paper, we derive new recurrence relations for two-variable orthogonal polynomials for example Jacobi polynomial, Bateman's polynomial and Legendre polynomial via two different differential operators $\Xi =\left(\frac{\partial }{\partial z}+\sqrt{w}\frac{\partial }{\partial w}\right)$ and $\Delta =\left(\frac{1}{w}\frac{\partial }{\partial z}+\frac{1}{z}\frac{\partial }{\partial w}\right)$. We also derive some special cases of our main results.

10 pages, 0 figure