Title

Jacobi Polynomials From Compatibility Conditions

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) α(1 + x) β, x ∈ [-1, 1], we show how to use the compatibility conditions to explicitly determine the recurrence coefficients of the monic Jacobi polynomials.

Publication Date

2-1-2005

Publication Title

Proceedings of the American Mathematical Society

Volume

133

Issue

2

Number of Pages

465-472

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9939-04-07566-5

Socpus ID

13544272009 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/13544272009

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