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generalized elliptic integrals

Proceedings of the Edinburgh Mathematical Society (1)

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SOME INEQUALITIES FOR THE GENERALIZED GRÖTZSCH FUNCTION
Xiaohui Zhang, Gendi Wang, Yuming Chu
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 51 / Issue 1 / February 2008

Published online by Cambridge University Press:

04 February 2008, pp. 265-272
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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.