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 t...

The method proposed here has been devised for solution of the spectral problem for the Lamé wave equation (see [2]), but extended lately to more general problems. This method is based on the phase function concept or the Prüfer angle determined by the Prüfer transformation cot θ(x) = y′(x)/y(x), where y(x) is a solution of a second order self-adjoint o.d.e. The Prüfer angle θ(x) has some useful...