Monotonicity and functional inequalities for the complete p-elliptic integrals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:453

Article

Zhang, Xiaohui¹ 

[1] Zhejiang Sci Tech Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China

关键词: Generalized trigonometric functions;    Generalized complete elliptic integrals;    Monotonicity;    Inequalities;   

DOI  :  10.1016/j.jmaa.2017.04.025

来源: Elsevier

【 摘 要 】

Takeuchi's generalized complete elliptic integrals related to generalized trigonometric functions are of importance in the computation of the generalized pi and in the elementary proof of Ramanujan's cubic transformation. In this paper we generalize some well-known results of the classical complete elliptic integrals to the case of Takeuchi's generalimd complete elliptic integrals. We obtain sharp monotonicity and convexity results for combinations of these functions, as well as functional inequalities. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free