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
Copyright Status
Unknown
Socpus ID
13544272009 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/13544272009
STARS Citation
Chen, Yang and Ismail, Mourad, "Jacobi Polynomials From Compatibility Conditions" (2005). Scopus Export 2000s. 4131.
https://stars.library.ucf.edu/scopus2000/4131