Results 11 to 20 of about 2,308 (173)
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
exaly +4 more sources
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
openaire +1 more source
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
doaj +1 more source
Univalence of Gaussian and confluent hypergeometric functions [PDF]
Proceedings of the American Mathematical Society, 1990 Conditions are determined for the univalence convexity and starlikeness of Gaussian and confluent hypergeometric functions. In addition, subordination results are obtained for these classes of functions.
Miller, Sanford S., Mocanu, Petru T.
openaire +2 more sources
Ray Transfer Matrix for Onion-Type GRIN Lenses [PDF]
EPJ Web of Conferences, 2022 We present the computation of an ABCD matrix for onion-type GRIN lenses. By applying a differential approximation of the layer thickness, the matrix product of a high number of matrices is synthetized into a single matrix where the elements are integrals.
Lockett Veronica +2 more
doaj +1 more source
Inequalities for Gaussian hypergeometric functions [PDF]
Journal of Mathematical Inequalities, 2017 Summary: In this paper, we first shall present some inequalities for Gaussian hypergeometric functions, which generalize an identity involving the inverse hyperbolic tangent function. Further, the monotonicity of general hypergeometric function is proved. The obtained results of this paper improve some known results.
Wang, Wen, Pan, Juanjuan, Yang, Shiguo
openaire +1 more source
Hypergeometric Series, Truncated Hypergeometric Series, and Gaussian Hypergeometric Functions [PDF]
, 2016 25 ...
Deines, Alyson +4 more
openaire +2 more sources
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
openaire +3 more sources
On Mathieu-type series for the unified Gaussian hypergeometric functions [PDF]
Applicable Analysis and Discrete Mathematics, 2020 The main purpose of this paper is to present closed integral form expressions for the Mathieu-type a-series and for the associated alternating versions whose terms contain a generalized p-extended Gauss' hypergeometric function. Related bounding inequalities for the p-generalized Mathieu-type series are also obtained.
Parmar, Rakesh K., Pogany, Tibor K.
openaire +4 more sources
Computation of certain integral formulas involving generalized Wright function
Advances in Difference Equations, 2020 The aim of the paper is to derive certain formulas involving integral transforms and a family of generalized Wright functions, expressed in terms of the generalized Wright hypergeometric function and in terms of the generalized hypergeometric function as
Nabiullah Khan +4 more
doaj +1 more source