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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On the maximum value of a confluent hypergeometric function [PDF]
Comptes Rendus. Mathématique, 2022 We study the maximum value of the confluent hypergeometric function with oscillatory conditions of parameters. As a consequence, we obtain new inequalities for the Gauss hypergeometric function.
Fejzullahu, Bujar Xh.
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Gauss Hypergeometric Representations of the Ferrers Function of the Second Kind [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 We derive all eighteen Gauss hypergeometric representations for the Ferrers function of the second kind, each with a different argument. They are obtained from the eighteen hypergeometric representations of the associated Legendre function of the second kind by using a limit representation.
Cohl, Howard S. +2 more
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Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function
Mathematics, 2021 The main aim of this research paper is to introduce a new extension of the Gauss hypergeometric function and confluent hypergeometric function by using an extended beta function.
Shilpi Jain +4 more
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Some Inequalities of Extended Hypergeometric Functions
Mathematics, 2021 Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent ...
Shilpi Jain +3 more
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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 ...
Paris, Richard B., Richard B. Paris
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Large parameter cases of the Gauss hypergeometric function [PDF]
Journal of Computational and Applied Mathematics, 2003 21 pages, 4 ...
Temme, Nico +4 more
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Product and Quotient of Independent Gauss Hypergeometric Variables
Ingeniería y Ciencia, 2011 In this article, we have derived the probability density functions of the productand the quotient of two independent random variables having Gauss hypergeometricdistribution.
Daya Krishna Nagar +1 more
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Modeling small-angle scattering data of porous and/or bicontinuous structures in <i>n</i> dimensions. [PDF]
J Appl CrystallogrA small‐angle scattering fitting function is derived for porous materials with arbitrary fractal dimension. It includes a correlation peak and a power law at higher q.Fractal structures are often observed in small‐angle scattering experiments where a simple power law q−α describes the scattering intensity over many orders of magnitude.
Frielinghaus H.
europepmc +2 more sources
Numerical Evaluation of the Gauss Hypergeometric Function with the hypergeo Package [PDF]
The R Journal, 2015 This paper introduces the hypergeo package of R routines for numerical calculation of hypergeometric functions. The package is focussed on efficient and accurate evaluation of the Gauss hypergeometric function over the whole of the complex plane within the constraints of fixed-precision arithmetic.
Hankin, Robin K. S.
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