On the algebraic independence of values of generalized hypergeometric functions

被引：5

作者：

Gorelov, V. A. ^{[1
]}

机构：

[1] Moscow Power Engn Inst, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2013年 / 94卷 / 1-2期

关键词：

generalized hypergeometric function; linear differential equation; algebraic independence of solutions; Galois group; differential field; transcendence degree; contiguous functions;

D O I：

10.1134/S0001434613070080

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider hypergeometric functions satisfying homogeneous linear differential equations of arbitrary order. We prove general theorems on the algebraic independence of the solutions of a set of hypergeometric equations as well as of the values of these solutions at algebraic points. The conditions of most theorems are necessary and sufficient.

引用

页码：82 / 95

页数：14

共 18 条

[1]

[Anonymous], 1953, HIGHER TRANSCENDENTA

[2] SIEGEL NORMALITY [J].