Approximate convexity and concavity of generalized Grötzsch ring function

被引：1

作者：

Wang Gendi

Qiu Songliang

Zhang Xiaohui

Chu Yuming

机构：

[1] Huzhou University,College of Science

[2] Zhejiang Sci-Tech University,College of Science

来源：

Applied Mathematics-A Journal of Chinese Universities | 2006年 / 21卷 / 2期

关键词：

33C05; generalized Grötzsch ring function; Ramanujan's modular equation; convexity; concavity;

D O I：

10.1007/BF02791357

中图分类号：

学科分类号：

摘要：

In this paper, the so-called approximate convexity and concavity properties of generalized Grötzsch ring function µα(r) by studying the monotonicity, convexity or concavity of certain composites of µα(r) are obtained.

引用

共 7 条

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Anderson G D(2000)Generalized elliptic integrals and modular equations Pacific J Math 1 1-37

[2]

Qiu S L(2000)Grötzsch ring and Ramanujan's modular equations Acta. Math Sinica 2 283-290

[3]

Vamanamurthy M K(1998)Singular values, quasiconformal maps and the Schottky upper bound Science in China Ser A 12 1241-1247

[4]

Qiu S L(1999)Infinite products and normalized quotients of hypergeometric functions SIAM J Math Anal 5 1057-1075

[5]

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