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Quadratic transformation inequalities for Gaussian hypergeometric function [PDF]
Journal of Inequalities and Applications, 2018 In the article, we present several quadratic transformation inequalities for Gaussian hypergeometric function and find the analogs of duplication inequalities for the generalized Grötzsch ring function.
Tie-Hong Zhao +3 more
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Axioms, 2023 Sanford S. Miller and Petru T. Mocanu’s theory of second-order differential subordinations was extended for the case of third-order differential subordinations by José A. Antonino and Sanford S. Miller in 2011.
Georgia Irina Oros +2 more
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Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities [PDF]
Symmetry, 2021 In their paper published in 1990, Miller and Mocanu have investigated the special function Gaussian hypergeometric function in view of its relation to the theory of analytic functions, stating conditions for this function to be univalent using a,b,c∈ℝ, c≠0,−1,−2,….
Georgia Irina Oros, Oros Georgia Irina
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Mathematics, 2023 The present research aims to present new results regarding the fundamental problem of providing sufficient conditions for finding the best subordinant of a third-order differential superordination. A theorem revealing such conditions is first proved in a
Georgia Irina Oros +1 more
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Generalized analysis of dynamic pull-in for singular magMEMS and MEMS oscillators [PDF]
Scientific ReportsThe exact pull-in threshold for single-degree-of-freedom actuator models arising in the design of micro-electro-mechanical systems (MEMS) is derived analytically by studying exact solutions to trinomial equations of arbitrary degree.
Piotr Skrzypacz +3 more
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Monotonicity and concavity properties of the Gaussian hypergeometric functions, with applications
Indian Journal of Pure and Applied Mathematics, 2022 Many fields of mathematics, such as mathematical physics, differential equations theory, number theory, complex analysis, hyperbolic geometry, statistics, and other disciplines have a long history of using hypergeometric functions of a single variable. For \(a, b\in\mathbb{C}\), and \(c\in\mathbb{C}\setminus\mathbb{Z}_0^{-}\), the Gauss hypergeometric ...
Miao-Kun Wang +2 more
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Sharp power mean bounds for the Gaussian hypergeometric function
Journal of Mathematical Analysis and Applications, 2005 Sharp inequalities are established between the Gaussian hypergeometric function and the power mean. These results extend known inequalities involving the complete elliptic integral and the hypergeometric mean.
Kendall Richards
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A reflection formula for the Gaussian hypergeometric function of matrix argument
Journal of Mathematical Analysis and Applications11 ...
Richards, Donald, Zheng, Qifu
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Inequalities for Gaussian hypergeometric functions [PDF]
Journal of Mathematical Inequalities, 2021 Summary: In this paper, the authors present several hypergeometric transformation inequalities for the Gaussian hypergeometric function \(F(a,b;c;x)\), which are the extensions of the known hypergeometric transformation identities such as Ramanujan's cubic transformation identities, by showing the monotonicity properties of certain quotients of \(F(a,b;
Ma, Xiao-Yan, Huang, Ti-Ren
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Three- and four-term recurrence relations for Horn's hypergeometric function $H_4$
Researches in Mathematics, 2022 Three- and four-term recurrence relations for hypergeometric functions of the second order (such as hypergeometric functions of Appell, Horn, etc.) are the starting point for constructing branched continued fraction expansions of the ratios of these ...
R.I. Dmytryshyn, I.-A.V. Lutsiv
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