Inequalities involving generalized Jacobian elliptic functions

被引：6

作者：

Neuman, Edward ^{[1
]}

机构：

[1] Math Res Inst, Carbondale, IL 62903 USA

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2014年 / 25卷 / 11期

关键词：

generalized Jacobian elliptic functions; generalized trigonometric functions; R-hypergeometric functions; convex/concave functions; inequalities; HUYGENS-TYPE INEQUALITIES; TRIGONOMETRIC FUNCTIONS; HYPERBOLIC FUNCTIONS; WILKER;

D O I：

10.1080/10652469.2014.937434

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the generalized Jacobian elliptic functions which play an important role in some bifurcation problems involving the p-Laplacian. A formula which connects three members of this family of functions is established. Computable bounds, the Wilker- and Huygens-type inequalities and other functional inequalities for the functions under discussion are also obtained. It is shown that the generalized Jacobian elliptic sine function is a multiplicatively concave function.

引用

页码：864 / 873

页数：10

共 34 条

[1]

[Anonymous], 2010, Handbook of Mathematical Functions

[2] INEQUALITIES FOR EIGENFUNCTIONS OF THE P-LAPLACIAN [J].