Explicit formulas for orthogonal polynomials derived from their difference equation

TL;DR

This paper derives explicit formulas for orthogonal polynomials by solving their difference equations with linear coefficients using the Momentenansatz, providing a direct method for their characterization.

Contribution

It introduces a novel application of the Momentenansatz to explicitly solve difference equations for orthogonal polynomials.

Findings

Explicit formulas for orthogonal polynomials are obtained.

The method simplifies deriving properties of orthogonal polynomials.

Provides a new approach to solving difference equations in orthogonal polynomial theory.

Abstract

We solve the difference equation with linear coefficients by the Momentenansatz to obtain explicit formulas for orthogonal polynomials.