Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials
Classical Analysis and ODEs
2017-03-30 v3 High Energy Physics - Theory
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
The multi-indexed Laguerre and Jacobi polynomials form a complete set of orthogonal polynomials. They satisfy second-order differential equations but not three term recurrence relations, because of the 'holes' in their degrees. The multi-indexed Laguerre and Jacobi polynomials have Wronskian expressions originating from multiple Darboux transformations. For the ease of applications, two different forms of simplified expressions of the multi-indexed Laguerre and Jacobi polynomials are derived based on various identities. The parity transformation property of the multi-indexed Jacobi polynomials is derived based on that of the Jacobi polynomial.
Keywords
Cite
@article{arxiv.1612.00927,
title = {Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:1612.00927},
year = {2017}
}