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Kovacic's algorithm and its application to some families of special functions

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Abstract

We apply the Kovacic algorithm to some families of special functions, mainly the hypergeometric one and that of Heun, in order to discuss the existence of closed-form solutions. We begin by giving a slightly modified version of the Kovacic algorithm and a sketch proof.

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Authors and Affiliations

  1. U.F.R. de Mathématiques, Université des Sciences et Techniques, F-59655, Villeneuve d'Ascq-Cedex, France

    Anne Duval

  2. Mathématiques, Université Paris 11, Bâtiment 425, F-91405, Orsay-Cedex, France

    Michèle Loday-Richaud

Authors
  1. Anne Duval
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  2. Michèle Loday-Richaud
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Duval, A., Loday-Richaud, M. Kovacic's algorithm and its application to some families of special functions. AAECC 3, 211–246 (1992). https://doi.org/10.1007/BF01268661

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  • DOI: https://doi.org/10.1007/BF01268661

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