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arXiv · 0706.3003

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

H. J. Weber
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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.

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H. J. Weber. 2007-06-20. Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula. https://arxiv.org/abs/0706.3003

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