ϵ-expansion of multivariable hypergeometric functions appearing in Feynman integral calculus
Nuclear Physics B, 2023 We present a new methodology, suitable for implementation on computer, to perform the ϵ-expansion of hypergeometric functions with linear ϵ dependent Pochhammer parameters in any number of variables.
Souvik Bera
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Implementation of summation theorems of Andrews and Gessel-Stanton
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 Generalized hypergeometric functions and their natural generalizations in one and several variables appear in many mathematical problems and their applications.
M.I. Qureshi, T.R. Shah
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$$\Gamma $$-evaluations of hypergeometric series
The Ramanujan Journal, 2022 AbstractIn this paper we explore special values of Gaussian hypergeometric functions in terms of products of Euler $$\Gamma $$ Γ -functions and exponential functions of linear functions of the hypergeometric parameters.
Frits Beukers, Jens Forsgård
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Summation formulas for Fox-Wright function [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 By means of inversion techniques and several known hypergeometric series identities, summation formulas for Fox-Wright function are explored. They give some new hypergeometric series identities when the parameters are specified.
Chuanan Wei, Lily Li Liu, Dianxuan Gong
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GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
Journal of High Energy Physics, 2023 We present the Gel’fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of the Feynman integrals of the three-loop vacuum diagrams with arbitrary masses, basing on Mellin-Barnes representations and Miller’s transformation. The codimension of derived GKZ
Hai-Bin Zhang, Tai-Fu Feng
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Derivatives of any Horn-type hypergeometric functions with respect to their parameters
Nuclear Physics B, 2020 We consider the derivatives of Horn hypergeometric functions of any number of variables with respect to their parameters. The derivative of such a function of n variables is expressed as a Horn hypergeometric series of n+1 infinite summations depending ...
Vladimir V. Bytev, Bernd A. Kniehl
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Independence polynomials and hypergeometric series [PDF]
Bulletin of the London Mathematical Society, 2021 Bulletin of the London Mathematical Society, 53 (6)
Radchenko, Danylo +1 more
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Analytical expression for the exact curved surface area and volume of hyperboloid of two sheets via Mellin-Barnes type contour integration [PDF]
Journal of Mahani Mathematical Research, 2023 In this article, we aim at obtaining the analytical expression (not previously found and recorded in the literature) for the exact curved surface area of a hyperboloid of two sheets in terms of Appell's double hypergeometric function of second kind and ...
M.A. Pathan, M. Qureshi, Javid Majid
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Hypergeometric Series, Truncated Hypergeometric Series, and Gaussian Hypergeometric Functions [PDF]
, 2016 25 ...
Deines, Alyson +4 more
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Logarithmic A-hypergeometric series [PDF]
International Journal of Mathematics, 2020 The method of Frobenius is a standard technique to construct series solutions of an ordinary linear differential equation around a regular singular point. In the classical case, when the roots of the indicial polynomial are separated by an integer, logarithmic solutions can be constructed by means of perturbation of a root.
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