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arXiv · 1612.00927

Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials

Satoru Odake·Ryu Sasaki
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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.

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BibTeXRIS

Satoru Odake, Ryu Sasaki. 2016-12-03. Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials. https://doi.org/10.3842/sigma.2017.020

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