Generalized 2D Laguerre polynomials and their quaternionic extensions

TL;DR

This paper introduces quaternionic extensions of bivariate orthogonal polynomials, explores their ladder operators via Cullen derivatives, and establishes summation and integral formulas with potential physical applications.

Contribution

It extends classical 2D Laguerre polynomials to quaternionic settings and analyzes their algebraic and analytical properties for the first time.

Findings

Quaternionic polynomials are constructed from classical bivariate polynomials.

Ladder operators are realized as differential operators using Cullen derivatives.

Summation and integral formulas are derived with potential physical relevance.

Abstract

The analogous quaternionic polynomials of a class of bivariate orthogonal polynomials (arXiv: 1502.07256, 2014) introduced. The ladder operators for these quaternionic polynomials also studied. For the quaternionic case, the ladder operators are realized as differential operators in terms of the so-called Cullen derivatives. Some physically interesting summation and integral formulas are proved, and their physical relevance is also briefly discussed.