%0 Journal Article
%T Some Sharp Inequalities for Generalized Grotzsch Ring Function<br>广义Grotzsch环函数的几个精确不等式
%A Zhang Xiaohui
%A Qiu Songliang
%A Chu Yuming
%A Wang Gendi
%A <br>张孝惠
%A 裘松良
%A 褚玉明
%A 王根娣
%J 数学物理学报(A辑)
%D 2008
%I 
%X For $a\in(0,1/2]$ and $r\in(0,1)$,let $\mu_a(r)$ be the so-called generalized Gr\"otzschring function which is defined by $\mu_a(r)=\pi\K'_a(r)]/2\sin(\pi a)\K_a(r)]$,appearing in Ramanujan's generalized modular equations.In this paper, the authors study the relations of the functions$\mu_a(r)$ and $\mu(r)$ and the monotonicity and convexity of combinations of the function $\mu_a(r)$ and some elementary functions, and obtain several sharpinequalities for $\mu_a(r)$. Some properties of the function $\mu(r)$ are generalized to the function $\mu_a(r)$.
%K Generalized elliptic integralszz
%K Generalized Gr"otzsch ring functionzz
%K Monotoniceityzz
%K Inequalitieszz<br>广义椭圆积分
%K 广义Grotzsch环函数
%K 单调性
%K 不等式.
%K 环函数
%K 不等式
%K Generalized
%K Inequalities
%K Function
%K 性质
%K 凸性
%K 单调性
%K 函数的组合
%K 初等
%K 关系
%K 研究
%K 模方程
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=4C373D0912D1D1E37DE50577A7D49850&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=CA4FD0336C81A37A&sid=6AC2A205FBB0EF23&eid=457934BE093FCE13&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=0&reference_num=10