Results 11 to 20 of about 17,203 (248)

Hypergeometric series representations of Feynman integrals by GKZ hypergeometric systems

Journal of High Energy Physics, 2020
We show that almost all Feynman integrals as well as their coefficients in a Laurent series in dimensional regularization can be written in terms of Horn hypergeometric functions.
René Pascal Klausen
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Decomposition formulas for some quadruple hypergeometric series

Қарағанды университетінің хабаршысы. Математика сериясы, 2020
In the present work, the authors obtained operator identities and decomposition formulas for second order Gauss hypergeometric series of four variables into products containing simpler hypergeometric functions. A Choi–Hasanov method based on the inverse
A.S. Berdyshev, A. Hasanov, A.R. Ryskan
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Matrix q-hypergeometric series

Discrete Mathematics, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Kung-Wei
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Special Values of the Hypergeometric Series [PDF]

Memoirs of the American Mathematical Society, 2017
In this paper, we present a new method for finding identities for hypergeoemtric series, such as the (Gauss) hypergeometric series, the generalized hypergeometric series and the Appell-Lauricella hypergeometric series. Furthermore, using this method, we get identities for the hypergeometric series
Akihito Ebisu, Ebisu, Akihito
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Exceptional sets of hypergeometric series

Journal of Number Theory, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Natália Archinard, Archinard, Natália
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Logarithmic A-hypergeometric series II [PDF]

, 2022
In this paper, following [6], we continue to develop the perturbing method of constructing logarithmic series solutions to a regular A-hypergeometric system. Fixing a fake exponent of an A-hypergeometric system, we consider some spaces of linear partial differential operators with constant coefficients.
Okuyama, Go, Saito, Mutsumi
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Summed Series Involving ₁F₂ Hypergeometric Functions [PDF]

Mathematics
Summation of infinite series has played a significant role in a broad range of problems in the physical sciences and is of interest in a purely mathematical context.
Jack C. Straton
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Rook Theory and Hypergeometric Series

Advances in Applied Mathematics, 1996
The author investigates generalizations of the ``hit'' numbers of rook theory, which are defined via cycle-counting rook placements as popularized by Chung and Graham. Extensions of results of Chow and Gessel are derived. For Ferrers boards, the author shows how to express these hit numbers as balanced, terminating hypergeometric series of a type ...
Haglund, James
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Factorization of Basic Hypergeometric Series

Symmetry, Integrability and Geometry: Methods and Applications
The general problem of the factorization of a basic hypergeometric series is presented and discussed. The case of the general $_2\psi_2$ series is examined in detail. Connections are found with the theory of basic hypergeometric series on root systems. Alternative proofs of several well-known summation and transformation formulae, including Gustafson's
Bradley-Thrush, Jonathan G.
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Modeling small-angle scattering data of porous and/or bicontinuous structures in <i>n</i> dimensions. [PDF]

J Appl Crystallogr
A 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.
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