Open problem in orthogonal polynomials

A. D. Alhaidari

Published 2017-09-16Version 1

Using an algebraic method for solving the wave equation in quantum mechanics, we encountered two new classes of orthogonal polynomials on the real line. Up to now, these polynomials are defined by their three-term recursion relations and initial values. However, their other properties like the weight functions, generating functions, orthogonality, Rodrigues-type formulas, etc. are yet to be derived analytically. Due to the prime significance of these polynomials in physics, we hope that experts in the field of orthogonal polynomials could study them, derive their properties and write them in closed form (e.g., in terms of hypergeometric functions).