Jacobi Polynomials from Compatibility Conditions
Classical Analysis and ODEs
2007-05-23 v1
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.
Cite
@article{arxiv.math/0302142,
title = {Jacobi Polynomials from Compatibility Conditions},
author = {Yang Chen and Mourad Ismail},
journal= {arXiv preprint arXiv:math/0302142},
year = {2007}
}
Comments
11 pages 0 figures