Solution of an Open Problem about Two Families of Orthogonal Polynomials

Abstract

An open problem about two new families of orthogonal polynomials was posed by Alhaidari. Here we will identify one of them as Wilson polynomials. The other family seems to be new but we show that they are discrete orthogonal polynomials on a bounded countable set with one accumulation point at 0 and we give some asymptotics as the degree tends to infinity.

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• Bound-state solutions of the Schrödinger equation for two novel potentials
• Electrostatic multipole contributions to the binding energy of electrons
• Progressive approximation of bound states by finite series of square-integrable functions