Results 1 to 10 of about 2,308 (173)
On Decomposition Formulas Related to the Gaussian Hypergeometric Functions in Three Variables [PDF]
Journal of Function Spaces, 2021 In this paper, by using certain inverse pairs of symbolic operators introduced by Choi and Hasanov in 2011, we establish several decomposition formulas associated with the Gaussian triple hypergeometric functions.
Anvar Hasanov, Jihad Younis, Hassen Aydi
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Modeling small-angle scattering data of porous and/or bicontinuous structures in <i>n</i> dimensions. [PDF]
J Appl CrystallogrA small‐angle scattering fitting function is derived for porous materials with arbitrary fractal dimension. It includes a correlation peak and a power law at higher q.Fractal structures are often observed in small‐angle scattering experiments where a simple power law q−α describes the scattering intensity over many orders of magnitude.
Frielinghaus H.
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On Certain Sufficient Condition Involving Gaussian Hypergeometric Functions
International Journal of Mathematics and Mathematical Sciences, 2009 The authors define a new subclass of 𝒜 of functions involving complex order in the open unit disk 𝕌. For this new class, we obtain certain inclusion properties involving the Gaussian hypergeometric functions.
H. Silverman, Thomas Rosy, S. Kavitha
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Univalence and Convexity Properties for Gaussian Hypergeometric Functions
Rocky Mountain Journal of Mathematics, 2001 Let \(f(z)=z+a_2z^2+ \cdots\) be analytic in the unit disk \(\mathbf{D}\). Then \(f(z)\) is called convex if it is univalent and \(f(\mathbf{D})\) is convex, and \(f(z)\) is called starlike if it is univalent and \(f(\mathbf D)\) is starlike with respect to the origin. Furthermore \(f(z)\) is called close-to-convex if there is a convex function \(g(z)\)
Saminathan Ponnusamy, M Vuorinen
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Copas-Heckman-Type Sensitivity Analysis for Publication Bias in Rare-Event Meta-Analysis Under Generalized Linear Mixed Models. [PDF]
Stat MedABSTRACT In systematic reviews and meta‐analyses, publication bias (PB) is one of the serious concerns and mainly induced by selective publication of academic literatures. Although many methods have been proposed to address PB, almost all of them are based on the normal‐normal (NN) random‐effects model, assuming that data are normally distributed at ...
Zhou Y +5 more
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Sufficiency for Gaussian hypergeometric functions to be uniformly convex [PDF]
International Journal of Mathematics and Mathematical Sciences, 1999 Let F(a,b;c;z) be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk 𝒰. Let an operator Ia,b;c(f) be defined by [Ia,b;c(f)](z)=zF(a,b;c;z)*f(z).
Yong Chan Kim, S. Ponnusamy
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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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Close-to-convexity properties of Gaussian hypergeometric functions
Journal of Computational and Applied Mathematics, 1998 Let \(F(a, b;c;z)\) be the classical hypergeometric function. The sufficient conditions on \(a\), \(b\), \(c\) under which \(zF(a,b; c,z)\) or \({c\over ab} [F(a, b; c;z)- 1]\) is closed-to-convex of order \(\beta\) in \(| z|< 1\) are given. Example: If \(a\in (0,\infty)\), \(b\in\left(0,{1\over a}\right]\) and if for some real \(\eta\), \(|\eta|< {\pi\
Saminathan Ponnusamy
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Moments of Gaussian hypergeometric functions over finite fields
Functiones Et Approximatio, Commentarii Mathematici, 2023 We prove explicit formulas for certain first and second moment sums of families of Gaussian hypergeometric functions $_{n+1}F_n$, $n\ge1$, over finite fields with $q$ elements where $q$ is an odd prime. This enables us to find an estimate for the value $_6F_5(1)$.
Mohammad Sadek
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