A generic classification of exceptional orthogonal X1-polynomials based on Pearson distributions family

Abstract

The so-called exceptional orthogonal X1-polynomials arise as eigen functions of a Sturm-Liouville problem. In this paper, a generic classification of these polynomials is presented based on Pearson distributions family. Then, six special differential equations of the aforesaid classification are introduced and their polynomial solutions are studied in detail.

arXiv comment24 pages

References in corpus (5)

• An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
• Infinitely many shape invariant potentials and new orthogonal polynomials
• An Extension of Bochner's Problem: Exceptional Invariant Subspaces
• Another set of infinitely many exceptional (X_{\ell}) Laguerre polynomials
• Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics