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A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments
AxiomsIn this paper, the authors briefly review some closed-form formulas of the Gauss hypergeometric function at specific arguments, alternatively prove four of these formulas, newly extend a closed-form formula of the Gauss hypergeometric function at some ...
Yue-Wu Li, Feng Qi
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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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New Series Expansions of the Gauss Hypergeometric Function [PDF]
Advances in Computational Mathematics, 2013 The Gauss hypergeometric function ${}_2F_1(a,b,c;z)$ can be computed by using the power series in powers of $z, z/(z-1), 1-z, 1/z, 1/(1-z),(z-1)/z$. With these expansions ${}_2F_1(a,b,c;z)$ is not completely computable for all complex values of $z$.
López, José Luis, Temme, Nico M.
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Asymptotics of the Gauss hypergeometric function with large parameters, I [PDF]
Journal of Classical Analysis, 2013 We obtain asymptotic expansions for the Gauss hypergeometric function F(a+ε1λ,b+ε2λ;c+ε3λ;z) as |λ| →∞ when the εj are finite by an application of the method of steepest descents, thereby extending previous results corresponding to εj = 0, ±1. By means of
Paris, Richard B.
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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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A New Extension of the τ-Gauss Hypergeometric Function and Its Associated Properties
Mathematics, 2019 In this article, we define an extended version of the Pochhammer symbol and then introduce the corresponding extension of the τ-Gauss hypergeometric function.
Hari Mohan Srivastava +4 more
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Journal of New Theory, 2022 The main objective of this paper is to use the newly proposed $(p,q;l)$-extended beta function to introduce the $(p,q;l)$-extended $τ$-Gauss hypergeometric and the $(p,q;l)$-extended $τ$-confluent hypergeometric functions with some of their properties ...
Umar Muhammad Abubakar
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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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Gauss’ Hypergeometric Function [PDF]
, 2007 We give a basic introduction to the properties of Gauss’ hypergeometric functions, with an emphasis on the determination of the monodromy group of the Gaussian hypergeometric equation.
F. Beukers
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Algebraic transformations of Gauss hypergeometric functions
Funkcialaj Ekvacioj, 2009 This article gives a classification scheme of algebraic transformations of Gauss hypergeometric functions, or pull-back transformations between hypergeometric differential equations.
Vidunas, Raimundas
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