Results 21 to 30 of about 2,865 (170)

Distribution of values of Gaussian hypergeometric functions

Pure and Applied Mathematics Quarterly, 2023
In the 1980's, Greene defined {\it hypergeometric functions over finite fields} using Jacobi sums. The framework of his theory establishes that these functions possess many properties that are analogous to those of the classical hypergeometric series studied by Gauss and Kummer.
Ono, Ken, Saad, Hasan, Saikia, Neelam
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EVALUATION OF THE NON-ELEMENTARY INTEGRAL \(\int e^{\lambda x^\alpha}dx\), \(\alpha\ge 2\), AND OTHER RELATED INTEGRALS

Ural Mathematical Journal, 2017
A formula for the non-elementary integral \(\int e^{\lambda x^\alpha} dx\) where \(\alpha\) is real and greater or equal two, is obtained in terms of the confluent hypergeometric function \(_{1}F_1\) by expanding the integrand as a Taylor series.
Victor Nijimbere
doaj   +1 more source

Inequalities for zero-balanced Gaussian hypergeometric functions [PDF]

Mathematical Inequalities & Applications, 2017
In this paper, we consider the monotonicity of certain combinations of the Gaussian hypergeometric functions $F(a-1,b;a+b;1-x^c)$ and $F(a-1-δ,b+δ;a+b;1-x^d)$ on $(0,1)$ for $δ\in(a-1,0)$, and study the problem of comparing these two functions, thus get the largest value $δ_1=δ_1(a,c,d)$ such that the inequality $F(a-1,b;a+b;1-x^c)
Huang, Ti-Ren, Ma, Xiao-Yan, Zhang, Xiao-Hui   +2 more
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Representation of Some Ratios of Horn’s Hypergeometric Functions H₇ by Continued Fractions

Axioms, 2023
The paper deals with the problem of representation of Horn’s hypergeometric functions via continued fractions and branched continued fractions. We construct the formal continued fraction expansions for three ratios of Horn’s hypergeometric functions H7 ...
Tamara Antonova, Roman Dmytryshyn, Pavlo Kril, Serhii Sharyn   +3 more
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On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H₄(a,b;c,d;z₁,z₂) Ratios

Axioms, 2023
The paper deals with the problem of representation of Horn’s hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn’s hypergeometric function H4 ratios are constructed.
Tamara Antonova, Roman Dmytryshyn, Ilona-Anna Lutsiv, Serhii Sharyn   +3 more
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Applications of Subordination Chains and Fractional Integral in Fuzzy Differential Subordinations

Mathematics, 2022
Fuzzy differential subordination theory represents a generalization of the classical concept of differential subordination which emerged in the recent years as a result of embedding the concept of fuzzy set into geometric function theory.
Georgia Irina Oros, Simona Dzitac
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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. Some transformation formulas for these functions have also been obtained.
Anvar Hasanov, Jihad Younis, Hassen Aydi
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Some exact Bradlow vortex solutions

Journal of High Energy Physics, 2017
We consider the Bradlow equation for vortices which was recently found by Manton and find a two-parameter class of analytic solutions in closed form on nontrivial geometries with non-constant curvature.
Sven Bjarke Gudnason, Muneto Nitta
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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 \(g(z)\)
Ponnusamy, S., Vuorinen, M.
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Monotonicity properties of Gaussian hypergeometric functions with respect to the parameter

Mathematical Inequalities & Applications, 2022
The authors establish the necessary and sufficient conditions under which certain combinations of Gaussian hypergeometric function and elementary function are monotone in the parameter, which generalize the recent results of generalized elliptic integrals of the first and second kinds obtained by Qiu et al.
Bao, Qi, Wang, Miao-Kun, Qiu, Song-Liang
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