Algebraicity of the Appell-Lauricella and Horn hypergeometric functions

Details Algebraicity of the Appell-Lauricella and Horn hypergeometric functions Algebraicity of the Appell-Lauricella and Horn hypergeometric functions

2010-05-03

arxiv.org/abs/1005.0317v2

Mathematics

Classical Analysis and ODEs

24 pages, 6 tables, 2 figures

Scientific paper

We extend Schwarz' list of irreducible algebraic Gauss functions to the four
classes of Appell-Lauricella functions in several variables and the 14 complete
Horn functions in two variables. This gives an example of a family of functions
such that for any number of variables there are infinitely many algebraic
functions, namely the Lauricella $F_C$ functions.

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