Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula
Classical Analysis and ODEs
2007-06-21 v1
Abstract
Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and an addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas. Applications to the classical polynomials are given.
Keywords
Cite
@article{arxiv.0706.3003,
title = {Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula},
author = {H. J. Weber},
journal= {arXiv preprint arXiv:0706.3003},
year = {2007}
}
Comments
13 pages, no figures