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.