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Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions [PDF]
, 2015 In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of `hypergeometric' algebraic varieties that are higher dimensional analogues of ...
Deines, Alyson +4 more
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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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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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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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Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems [PDF]
, 2020 Multidimensional matrix inversions provide a powerful tool for studying multiple hypergeometric series. In order to extend this technique to elliptic hypergeometric series, we present three new multidimensional matrix inversions.
Rosengren, Hjalmar +1 more
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SOME PROPERTIES OF HORN TYPE SECOND ORDER DOUBLE HYPERGEOMETRIC SERIES [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2018 Horn [1931, Hypergeometrische Funktionen zweier Veranderlichen, Math. Ann.,105(1), 381-407], (corrections in Borngasser [1933, Uber hypergeometrische funkionen zweier Veranderlichen, Dissertation, Darmstadt], defined and investigated ten second order ...
Anvar Hasanov +2 more
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International Journal of Mathematics for Industry, 2023 Fractional kinetic equations are of immense importance in describing and solving numerous intriguing problems of physics and astrophysics. Inequalities are important topics in special functions.
Ankita Chandola, Rupakshi Mishra Pandey
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