Results 21 to 30 of about 2,308 (173)
On Gaussian Hypergeometric Functions of Three Variables: Some New Integral Representations
Journal of Mathematics, 2022 The present paper establishes several new integral representations of the Euler type and Laplace type for some Gauss hypergeometric functions of three variables. The main results are obtained by using the properties of Gamma and beta functions. The novel
Maged G. Bin-Saad +4 more
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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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Lightcone expansions of conformal blocks in closed form
Journal of High Energy Physics, 2020 We present new closed-form expressions for 4-point scalar conformal blocks in the s- and t-channel lightcone expansions. Our formulae apply to intermediate operators of arbitrary spin in general dimensions.
Wenliang Li
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Quantitative versions of the two-dimensional Gaussian product inequalities
Journal of Inequalities and Applications, 2023 The Gaussian product-inequality (GPI) conjecture is one of the most famous inequalities associated with Gaussian distributions and has attracted much attention.
Ze-Chun Hu, Han Zhao, Qian-Qian Zhou
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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 +3 more
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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 +2 more
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Inequalities of extended beta and extended hypergeometric functions
Journal of Inequalities and Applications, 2017 We study the log-convexity of the extended beta functions. As a consequence, we establish Turán-type inequalities. The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended beta ...
Saiful R. Mondal
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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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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 +3 more
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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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