Landen inequalities for a class of hypergeometric functions with applications

By Miao-Kun Wang, Y. Chu. 2018

67 citations recorded by the source corpus.

In this paper, we study a class of Gaussian hypergeometric function 2F1(a,b;(a+b+ 1)/2;x)(a,b > 0) , and find the maximal regions of ab plane in the first quadrant where the wellknown Landen identities for the complete elliptic integrals of the first kind turn on respective inequalities valid for each x ∈ (0,1) . Besides, the generalized Grötzsch ring function with two parameters μa,b(r) is introduced, and the analogs of duplication formula satisfied by Grötzsch ring function μ(r) for μa,b(r) , in the form of inequalities, will be derived. Mathematics subject classification (2010): 33E05, 33C05.

Subfields: Applied Mathematics, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/5e0d2419af6d53b4f1745dd611ca2d8601e98937

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In Applied Mathematics

1. Y. Chu
2. Tie-hong Zhao
3. Jingfeng Tian
4. Zhen-Hang Yang
5. Zhonghua Shen
6. Miao-Kun Wang
7. Wei-Mao Qian
8. Saima Rashid

In Sociology and Political Science

1. Zhen-Hang Yang
2. Jingfeng Tian
3. Tie-hong Zhao
4. Y. Chu

Citations in the corpus

• Convexity and monotonicity for elliptic integrals of the first kind and applications (2017, methodology): “Recently, it was applied preliminarily to certain special functions, for example, trigonometric and hyperbolic functions [44],Toader-Qi mean [45] (see also [46], [47]), generalized elliptic integrals [43, 48], hypergeometric functions [49], Bessel functions [50, 51].”
• Sharp power mean bounds for the lemniscate type means (2021, background): “[17] Wang, M-K; Chu, Y-M, Landen inequalities for a class of hypergeometric functions with applications, Math.”