Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

Details Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

2007-06-20

arxiv.org/abs/0706.3003v1

Central European J. Math. 5 (2007) 415-427

Mathematics

Classical Analysis and ODEs

13 pages, no figures

Scientific paper

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.

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