Inequalities for Jacobian elliptic functions and Gauss lemniscate functions

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• 作者：Edward Neuman ^{edneuman@siu.edu}
• 关键词：Jacobian elliptic functions ; Gauss lemniscate functions ; Inverse functions ; Completely symmetric elliptic integral of the first kind ; Bivariate means ; Inequalities
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：1 April, 2012
• 卷：218
• 期：15
• 页码：7774-7782
• 文件大小：197 K

摘要

A new proof of inequalities involving Jacobian elliptic functions and their inverse functions are obtained. Similar results for the Gauss lemniscate functions are also established. Upper bounds for the inverse Jacobian elliptic functions and for the Gauss arc lemniscate functions are derived.