Generalized 2D Laguerre polynomials and their quaternionic extensions

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.