Gauss hypergeometric function: reduction, ε-expansion for integer/half-integer parameters and Feynman diagrams [PDF]
, 2006 The Gauss hypergeometric functions 2F1 with arbitrary values of parameters are reduced to two functions with fixed values of parameters, which differ from the original ones by integers.
M. Kalmykov
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New series expansions of the Gauss hypergeometric function [PDF]
Advances in Computational Mathematics, 2013 The Gauss hypergeometric function 2F1(a,b,c;z) can be computed by using the power series in powers of $z, z/(z-1), 1-z, 1/z, 1/(1-z),~\textrm{and}~(z-1)/z$. With these expansions, 2F1(a,b,c;z) is not completely computable for all complex values of z.
J. López, N. Temme
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On the generalized Gauss hypergeometric function
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2008 In this work the (τ, β)-hypergeometric Gauss function is considered, the basic properties of this function are investigated, some applications are given.
N. A. Virchenko
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ASYMPTOTICS OF A GAUSS HYPERGEOMETRIC FUNCTION WITH TWO LARGE PARAMETERS: A NEW CASE
The ANZIAM Journal, 2019 Asymptotic expansions of the Gauss hypergeometric function with large parameters, $F(\unicode[STIX]{x1D6FC}+\unicode[STIX]{x1D716}_{1}\unicode[STIX]{x1D70F},\unicode[STIX]{x1D6FD}+\unicode[STIX]{x1D716}_{2}\unicode[STIX]{x1D70F};\unicode[STIX]{x1D6FE ...
J. Harper
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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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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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Numerical Evaluation of the Gauss Hypergeometric Function with the hypergeo Package
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 ...
R. Hankin
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A Note on Wright-type Generalized q-hypergeometric Function
Известия Иркутского государственного университета: Серия "Математика"In 2001, Virchenko et al. published a paper on a new generalization of Gauss hypergeometric function, namely Wright-type generalized hypergeometric function. Present work aims to define the q-analogue generalized hypergeometric function, which reduces to
K. K. Chaudhary, S. B. Rao
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Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions
Integral transforms and special functions, 2018 We consider the hypergeometric function for . For , we derive a convergent expansion of in terms of the function and of rational functions of z that is uniformly valid for z in any compact in . When , the expansion also contains a logarithmic term of the
Chelo Ferreira +2 more
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Jaccard dissimilarity in stochastic community models based on the species‐independence assumption
Ecography, EarlyView.A fundamental problem in ecology is understanding the changes in species composition among sites (i.e. beta‐diversity). It is unclear how spatial heterogeneity in species occupancy across sites shapes patterns of beta‐diversity. To address this question, we develop probabilistic models that consider two spatial or temporal sites, where presence ...
Ryosuke Iritani +5 more
wiley +1 more source