On a Symmetric Generalization of Bivariate Sturm–Liouville Problems

Abstract A new class of partial differential equations having symmetric orthogonal solutions is presented. The general equation presented and orthogonality obtained using the Sturm–Liouville approach. Conditions on polynomial coefficients to have admissible are given. case analyzed in detail, providing weight function, three-term recurrence relations for monic solutions, as well explicit form these which an potentially self-adjoint linear second-order hypergeometric type.