Results 41 to 50 of about 12,448 (236)
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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Interpolation on Gauss hypergeometric functions with an application [PDF]
Involve, a Journal of Mathematics, 2018 To appear in Involve-A Journal of Mathematics, 16 ...
Hina Manoj Arora, Swadesh Kumar Sahoo
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Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x) [PDF]
, 2010 We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2 F r+1(x) when there are additional numeratorial and denominatorial ...
Miller, A. R., Paris, Richard B.
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Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z)
Kuwait Journal of Science, 2023 The role which hypergeometric functions have in the numerical and symbolic calculation, especially in the fields of applied mathematics and mathematical physics motivated research in this paper.
Gradimir V. Milovanović +2 more
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A generalization of Clausen's identity
, 2009 The paper aims to generalize Clausen's identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce to 3F2 series ...
G.E. Andrews +6 more
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Solar structure in terms of Gauss' hypergeometric function [PDF]
Astrophysics and Space Science, 1995 Hydrostatic equilibrium and energy conservation determine the conditions in the gravitationally stabilized solar fusion reactor. We assume a matter density distribution varying non-linearly through the central region of the Sun. The analytic solutions of the differential equations of mass conservation, hydrostatic equilibrium, and energy conservation ...
Haubold, H. J., Mathai, A. M.
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Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function
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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Extended Riemann-Liouville type fractional derivative operator with applications
Open Mathematics, 2017 The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind.
Agarwal P., Nieto Juan J., Luo M.-J.
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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.
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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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