Gauss超几何函数的导数和广义Legendre关系

Derivatives and Generalized Legendre's Relation of the Gaussian Hypergeometric Function

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.