摘要
本文将完全椭圆积分的导数公式及Legendre关系推广到Gauss超几何函数F(a,b;c;x),从而为研究F(a,b;c;x)、广义Grtzsch环函数μa(r)(由式5定义)以及Ramanujan理论提供了重要的工具。此外,本文还获得了F(a,b;c;x)和μa(r)的若干不等式。
In this paper, the author generalizes the derivative formulas and Legendre's reation of the comlete elliptic integrals to the Gaussian hypefgeometric function F(a, b; c; x ), thus provid-ing useful eds for the study of F(a, b; c; x ), the generalized Gr tzsch - ring function μa (r ) defined by (5), and Ramanujan's theory. In addition, several inequalities and some other prop-erties of F(a, b; c; x ) and μa (r) are obtained.