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.