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2007 | 5 | 2 | 415-427
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Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

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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 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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