Monotonicity and inequalities involving zero-balanced hypergeometric function
By Miao-Kun Wang, Y. Chu, E. Zhang. Mathematical Inequalities & Applications, 2019
86 citations recorded by the source corpus.
In the article, we present a monotonicity property involving the zero-balanced hypergeometric function F(a,b;a+ b;x) for all a,b > 0 , and establish several sharp inequalities for F(a,b;a+b;x) in the first quadrant of ab -plane, which are the generalizations of the previously results. Mathematics subject classification (2010): 33C05, 33E05.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/a51afc2353097a4f1968444f423b6e2c1791ae7f
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In Applied Mathematics
Citations in the corpus
- Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means (2020, background): “is the complete elliptic integral of the second kind [12,18,30,38,44,50,52] and it is the special case of the Gaussian hypergeometric function [31,41,42,49,57]”
- Inequalities for generalized trigonometric and hyperbolic functions with one parameter (2020, background): “…of mathematics [2, 3, 14, 17, 19, 20, 25, 30, 32, 35, 38, 41, 46, 50, 52, 61, 70, 74, 77, 81, 83, 85, 86, 87, 88], they are closely related to the bivariate means [15, 26, 54, 55, 56, 68, 73, 75, 78] and special functions [1, 7, 12, 13, 21, 22, 27, 28, 36, 51, 57, 58, 59, 60, 62, 65, 69, 72, 82].”
- Sharp power mean bounds for the lemniscate type means (2021, unknown): “018 [19] Wang, M-K; Chu, Y-M; Zhang, W.”
- Answers to three conjectures on convexity of three functions involving complete elliptic integrals of the first kind (2020, background): “where F (a, b; c;x) is the Gaussian hypergeometric function [2, 47, 48] given by”