Explicit formulas for parametrized families of irreducible algebraic Appell, Lauricella and Horn functions

2013/04/09 by Esther Bod, Bod, Esther
Mathematics · #33C65 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:33C65

paper · pdf · doi:10.48550/arxiv.1304.2540

11 pages

arxiv created 2013/04/09 · arxiv updated 2013/04/10

Abstract

For suitable choices of the parameters the Appell, Lauricella and Horn functions are algebraic. In a previous paper we showed that there exist families of algebraic functions for the F₄, F_C, G₃, H₄, H₅ and H₇ functions, depending on one parameter r. For each of these we give a solution of the form f^r.g of the system of differential equations and give formulas for f and g.

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