Jacobi Polynomials from Compatibility Conditions

2003/02/12 by Yang Chen, Mourad E. H. Ismail, Mourad Ismail +2 · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #math.CA

paper · pdf · doi:10.48550/arxiv.math/0302142

11 pages 0 figures

arxiv created 2003/02/12 · openalex publication_date 2003/02/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revisit the ladder operators for orthogonal polynomials and re-interpret two supplementary conditions as compatibility conditions of two linear over-determined systems; one involves the variation of the polynomials with respect to the variable z (spectral parameter) and the other a recurrence relation in n (the lattice variable). For the Jacobi weight w(x) = (1-x)^a(1+x)^b, x in [-1,1],we show how to use the compatibility conditions to explicitly determine the recurrence coefficients of the monic Jacobi polynomials.

Citations

• Orthogonal polynomials and their derivatives, I

Cited by

• Ladder Operators for Laguerre-type and Jacobi-type Orthogonal Polynomials

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