Results 1 to 10 of about 3,001,317 (197)
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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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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Moments of Gaussian hypergeometric functions over finite fields [PDF]
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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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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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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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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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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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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Distribution of the Hessian values of Gaussian hypergeometric functions
Ramanujan JournalAbstract We consider a special family of Gaussian hypergeometric functions whose entries are cubic and trivial characters over finite fields. The special values of these functions are known to give the Frobenius traces of families of Hessian elliptic curves.
Ken Ono, Neelam Saikia, Hasan Saad
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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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