Algebraicity of the Appell–Lauricella and Horn hypergeometric functions
Copyright policy )Algebraicity of the Appell–Lauricella and Horn hypergeometric functions
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.
24 pages, 6 tables, 2 figures
- Utrecht University Netherlands
- Utrecht University Netherlands
hypergeometric function, 33C65, Algebraic function, Appell-Lauricella function, Horn function, Appell–Lauricella function, algebraic function, Appell, Horn and Lauricella functions, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hypergeometric function, Analysis
hypergeometric function, 33C65, Algebraic function, Appell-Lauricella function, Horn function, Appell–Lauricella function, algebraic function, Appell, Horn and Lauricella functions, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hypergeometric function, Analysis
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