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Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials

Published 3 Dec 2016 in math.CA, hep-th, math-ph, math.MP, and nlin.SI | (1612.00927v3)

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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Authors (2)

  1. Satoru Odake 
  2. Ryu Sasaki 

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