Algebraicity of the Appell-Lauricella and Horn hypergeometric functions

作者：Bod E^*

来源：Journal of Differential Equations, 2012, 252(1): 541-566.

DOI：10.1016/j.jde.2011.09.023

• Hypergeometric function
• Algebraic function
• Appell-Lauricella function
• Horn function

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 ill 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.

• 出版日期2012-1-1