Results 11 to 20 of about 60,960 (218)
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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GKZ-hypergeometric systems for Feynman integrals
Nuclear Physics B, 2020 Basing on the systems of linear partial differential equations derived from Mellin-Barnes representations and Miller's transformation, we obtain GKZ-hypergeometric systems of one-loop self energy, one-loop triangle, two-loop vacuum, and two-loop sunset ...
Tai-Fu Feng +3 more
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A General Family of q-Hypergeometric Polynomials and Associated Generating Functions
Mathematics, 2021 Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of ...
Hari Mohan Srivastava, Sama Arjika
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A note on a generalization of Riordan's combinatorial identity via a hypergeometric series approach [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this note, an attempt has been made to generalize the well-known and useful Riordan's combinatorial identity via a hypergeometric series approach.
Dongkyu Lim
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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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Some Integrals Connected with a New Quadruple Hypergeometric Series
Universal Journal of Mathematics and Applications, 2020 Hypergeometric function of four variables was introduced by Bin-Saad and Younis. In the present paper a new integral representations of of Euler-type and Laplace-type involving double and triple hypergeometric series for these functions are derived.
Jihad Younis, Maged Bin-saad
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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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Derivatives of Horn-type hypergeometric functions with respect to their parameters [PDF]
, 2017 We consider the derivatives of Horn hypergeometric functions of any number variables with respect to their parameters. The derivative of the function in $n$ variables is expressed as a Horn hypergeometric series of $n+1$ infinite summations depending on ...
Bytev, V., Kniehl, B., Moch, S.
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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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Some Summation Theorems for Generalized Hypergeometric Functions
Axioms, 2018 Essentially, whenever a generalized hypergeometric series can be summed in terms of gamma functions, the result will be important as only a few such summation theorems are available in the literature. In this paper, we apply two identities of generalized
Mohammad Masjed-Jamei, Wolfram Koepf
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