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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A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments [PDF]
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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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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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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Further study on the conformable fractional Gauss hypergeometric function [PDF]
AIMS Mathematics, 2021 This article presents an exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric differential equation (CFGHDE) about the fractional regular singular points
Mahmoud Abul-Ez +2 more
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Multiple orthogonal polynomials with respect to Gauss' hypergeometric function [PDF]
Studies in applied mathematics (Cambridge), 2021 A new set of multiple orthogonal polynomials of both type I and type II with respect to two weight functions involving Gauss' hypergeometric function on the interval (0,1) is studied.
Hélder Lima, Ana F. Loureiro
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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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Multidomain spectral method for the Gauss hypergeometric function [PDF]
Numerical Algorithms, 2018 We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius’ method and Moebius transformations in the vicinity of each of the singular ...
S. Crespo +4 more
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Obtaining generating relations associated with the generalized Gauss hypergeometric function
University of Aden Journal of Natural and Applied Sciences, 2018 In this paper, some new generating relations involving the generalized hyper- geometric function and the generalized confluent hypergeometric function are established by mainly applying Taylor's Theorem. Due to their very general nature, the main results
Fadhle B. F. Mohsen, Maisoon Ahmed Kulib
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Integral Representations of Ratios of the Gauss Hypergeometric Functions with Parameters Shifted by Integers [PDF]
Mathematics, 2022 Given real parameters a,b,c and integer shifts n1,n2,m, we consider the ratio R(z)=2F1(a+n1,b+n2;c+m;z)/2F1(a,b;c;z) of the Gauss hypergeometric functions.
Alexander Dyachenko, Dmitrii Karp
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