Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula |
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Authors: | Hans J Weber |
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Institution: | (1) Department of Physics, University of Virginia, Charlottesville, VA 22904, USA |
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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 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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Keywords: | Polynomials with Rodrigues formula solutions of hypergeometric-type differential equation generating function in closed form recursion relations addition theorem |
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