Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials

Symmetry Integrability and Geometry-Methods and Applications

article

Satoru Odake¹  Ryu Sasaki¹ 

[1] Faculty of Science, Shinshu University

关键词: multi-indexed orthogonal polynomials;    Laguerre and Jacobi polynomials;    Wronskian formula;    determinant formula;   

DOI  :  10.3842/SIGMA.2017.020

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown