English

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