Simplified Expressions of the Multi-indexed Laguerre and Jacobi Polynomials

Satoru Odake, Ryu Sasaki

Published 2016-12-03Version 1

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.