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SOME INEQUALITIES FOR THE GENERALIZED GRÖTZSCH FUNCTION

Published online by Cambridge University Press:  04 February 2008

Xiaohui Zhang ,
Gendi Wang  and
Yuming Chu
Xiaohui Zhang
Affiliation:
Department of Mathematics, Huzhou University, Huzhou 313000, China (xhzhang@hutc.zj.cn)
Gendi Wang
Affiliation:
Department of Mathematics, Huzhou University, Huzhou 313000, China (xhzhang@hutc.zj.cn)
Yuming Chu
Affiliation:
Department of Mathematics, Huzhou University, Huzhou 313000, China (xhzhang@hutc.zj.cn)
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Abstract

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For $a\in(0,\tfrac12]$ and $r\in(0,1)$, let $\mu_a(r)$ be the so-called generalized Grötzsch function which appears in Ramanujan's generalized modular equations. In this paper, several sharp inequalities for $\mu_a(r)$ are obtained and a conjecture on $\mu_a(r)$, which was presented by Qiu and Vuorinen in 1999, is proved.

Keywords

Primary 33E0533C05generalized elliptic integralsgeneralized Grötzsch functionmonotonicityinequalities
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 1 , February 2008 , pp. 265 - 272
Copyright
Copyright © Edinburgh Mathematical Society 2008