Search Results - Gauss and basic hypergeometric functions

Geometric properties of basic hypergeometric functions by Agrawal, S., Sahoo, S.K.

“…In this article, we consider basic hypergeometric functions introduced by Heine. We study the mapping properties of certain ratios of basic hypergeometric…”
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The basic Gauss hypergeometric matrix function and its matrix q-difference equation by Salem, Ahmed

“…In this paper, the basic Gauss hypergeometric matrix function is introduced and studied…”
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A New Extension of the τ-Gauss Hypergeometric Function and Its Associated Properties by Srivastava, Hari Mohan, Tassaddiq, Asifa, Rahman, Gauhar, Nisar, Kottakkaran Sooppy, Khan, Ilyas

“…-Gauss hypergeometric function. The basic properties of the extended τ-Gauss hypergeometric function, including integral and derivative formulas involving the Mellin transform and the operators of fractional calculus, are derived…”
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A New Extension of the Pochhammer Symbol and Its Application to Hypergeometric Functions by Safdar, Maryam, Rahman, Gauhar, Ullah, Zafar, Ghaffar, Abdul, Nisar, Kottakkaran Sooppy

“… Also, we establish the basic properties and results for the extended τ -Gauss hypergeometric function, which includes integral and derivative formulas involving the Mellin transform and fractional calculus approaches…”
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Inequalities for Basic Special Functions Using Hölder Inequality by Masjed-Jamei, Mohammad, Moalemi, Zahra, Saad, Nasser

“…)|1q, and show that many basic special functions, such as the gamma and polygamma functions, Riemann zeta function, beta function and Gauss and confluent hypergeometric functions, satisfy this type of inequality…”
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On degenerate gamma matrix functions and related functions by Akel, Mohamed, Bakhet, Ahmed, Abdalla, Mohamed, He, Fuli

“… polygamma matrix function and the degenerate Gauss hypergeometric matrix function. Basic properties of these functions are discussed…”
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Some results involving generalized associated Legendre functions by Kalla, S. L., Virchenko, N., Lisetska, O.

“…In this paper, a new generalization of the associated Legendre functions of the first and the second kinds is introduced using the r-generalized Gauss hypergeometric function…”
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Extended Gauss Hypergeometric Matrix Functions by Abdalla, Mohamed, Bakhet, A

“…An extension of the Beta matrix function by introducing an extra matrix parameter is applied here to extend the Gauss and Kummer hypergeometric matrix functions…”
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Laguerre–Freud Equations for the Gauss Hypergeometric Discrete Orthogonal Polynomials by Fernandez-Irisarri, Itsaso, Manas, Manuel

“…The Cholesky factorization of the moment matrix is considered for the Gauss hypergeometric discrete orthogonal polynomials…”
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On the generalized Gauss hypergeometric function by N. A. Virchenko

“…In this work the (τ, β)-hypergeometric Gauss function is considered, the basic properties of this function are investigated, some applications are given…”
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A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments by Li, Yue-Wu, Qi, Feng

“…In 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…”
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The Gauss hypergeometric Gleser distribution with applications to flood peaks exceedance and income data by Olmos, Neveka M., Gómez-Déniz, Emilio, Venegas, Osvaldo

“…We introduced the Gauss hypergeometric Gleser (GHG) distribution, a novel extension of the Gleser (G…”
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Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function by Kim, Taekyun, Kim, Dae San, Jang, Lee-Chae, Lee, Hyunseok, Kim, Hanyoung

“…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…”
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Hybrid Algorithm via Reciprocal-Argument Transformation for Efficient Gauss Hypergeometric Evaluation in Wireless Networks by Cai, Jianping, Ying, Zuobin

“… To facilitate research, we introduce a computational framework tailored for the zero-balanced Gauss hypergeometric function Ψ(x,y)≜F12(1,x;1+x;−y…”
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A novel Kind of the multi-index Beta, Gauss, and confluent hypergeometric functions by Ali, Musharraf, Ghayasuddin, Mohd, A. Khan, Waseem, Nisar, Kottakkaran Sooppy

“… We also introduce a novel expansion of Gauss and confluent hypergeometric functions for our newly initiated beta function…”
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The Gauss hypergeometric covariance kernel for modeling second-order stationary random fields in Euclidean spaces: its compact support, properties and spectral representation by Emery, Xavier, Alegría, Alfredo

“… -dimensional Euclidean space. Both the covariance and its spectral density have an analytic expression involving the hypergeometric functions 2 F 1 and 1 F 2 , respectively, and four real-valued parameters related…”
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The Cădariu-Radu Method for Existence, Uniqueness and Gauss Hypergeometric Stability of Ω-Hilfer Fractional Differential Equations by Aderyani, Safoura, Saadati, Reza, Fečkan, Michal

“…Using the Cădariu–Radu method derived from the Diaz–Margolis theorem, we study the existence, uniqueness and Gauss hypergeometric stability of Ω…”
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A generic inequality for basic special functions by Masjed-Jamei, Mohammad

“…We introduce a generic inequality of the form and show that many special functions such as gamma and polygamma functions, Riemann zeta function, beta and incomplete beta functions, Gauss and confluent…”
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Integral Representations of Ratios of the Gauss Hypergeometric Functions with Parameters Shifted by Integers by Dyachenko, Alexander, Karp, Dmitrii

“…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…”
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Matrix continued fraction representation of the Gauss hypergeometric function by Mennou, S, Salhi, S, Kacha, A

“…]). Since calculations involving matrix valued functions with matrix arguments are feasible with large computers, it will be interesting attempt to develop such matrix theory…”
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