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

  • Research Article
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Central European Journal of Mathematics

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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Authors and Affiliations

  1. Department of Physics, University of Virginia, Charlottesville, VA, 22904, USA

    Hans J. Weber

Authors
  1. Hans J. Weber
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Cite this article

Weber, H.J. Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula. centr.eur.j.math. 5, 415–427 (2007). https://doi.org/10.2478/s11533-007-0004-6

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  • DOI: https://doi.org/10.2478/s11533-007-0004-6

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