Results 1 to 10 of about 614 (214)
Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function [PDF]
Advances in Difference Equations, 2021 A new family of p-Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help of the Gauss hypergeometric function.
Taekyun Kim +4 more
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Algebraic Transformations of Gauss Hypergeometric Functions
Funkcialaj Ekvacioj, 2009 Comment: 29 pages; 3 tables; Uniqueness claims and Remark 7.1 clarified by footnotes; formulas (28), (29 ...
Raimundas Vidūnas
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Gauss hypergeometric function and quadratic R-matrix algebras [PDF]
St. Petersburg mathematical journal, 1993 We consider representations of quadratic $R$-matrix algebras by means of certain first order ordinary differential operators. These operators turn out to act as parameter shifting operators on the Gauss hypergeometric function and its limit cases and on classical orthogonal polynomials. The relationship with W.
Koornwinder, T.H., Kuznetsov, V.B.
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Explicit Expressions for Most Common Entropies [PDF]
Entropy, 2023 Entropies are useful measures of variation. However, explicit expressions for entropies available in the literature are limited. In this paper, we provide a comprehensive collection of explicit expressions for four of the most common entropies for over ...
Saralees Nadarajah, Malick Kebe
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Hermite-Hadamard inequalities involving the Gauss hypergeometric function
AIP Conference Proceedings, 2018 The goal of this study is obtained the new generalization Hermite-Hadamard-Fejer inequalities involving the Gauss hypergeometric function. The results presented here would provide some fractional inequalities involving Saigo, Erdelyi-Kober and Riemann-Liouville type fractional operators.
Mehmet Zeki Sarıkaya
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Asymptotics of the Gauss hypergeometric function with large parameters, II [PDF]
Journal of Classical Analysis, 2013 Summary: We obtain asymptotic expansions for the Gauss hypergeometric function \[ F(a +\varepsilon_1\lambda,\,b +\varepsilon_2\lambda;\,c+\varepsilon_3\lambda;\,z) \] as \(|\lambda|\rightarrow\infty\) when the \(\varepsilon_j\) are finite by an application of the method of steepest descents, thereby extending previous results corresponding to ...
R. B. Paris
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TRANSFORMATIONS AND INVARIANTS FOR DIHEDRAL GAUSS HYPERGEOMETRIC FUNCTIONS
Kyushu Journal of Mathematics, 2012 Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a generalization of Clausen's formula and terminating double hypergeometric sums.
Raimundas Vidūnas
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New series expansions of the Gauss hypergeometric function [PDF]
Advances in Computational Mathematics, 2012 18 pages, 6 figures, 4 tables. In Advances in Computational Mathematics, 2012 Second version with corrected typos in equations (18) and (19)
López, José L., Temme, Nico M.
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On Extensions of Extended Gauss Hypergeometric Function
Communications in Advanced Mathematical Sciences, 2019 The aim of this paper is to introduce a new extensions of extended Gauss hypergeometric function. Certain integral representations, transformation and summation formulas for extended Gauss hypergeometric function are presented and some special cases are ...
Ahmed Ali Atash +2 more
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CERTAIN RESULTS ON EXTENDED GENERALIZED τ-GAUSS HYPERGEOMETRIC FUNCTION
Honam Mathematical Journal, 2016 Summary: The main aim of this paper is to introduce an extension of the generalized \(\tau\)-Gauss hypergeometric function \({}_rF^{\tau}_s(z)\) and investigate various properties of the new function such as integral representations, derivative formulas, Laplace transform, Mellin transform and fractional calculus operators.
Kumar, Dinesh +2 more
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