$$\Gamma $$-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
openaire +3 more sources
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
doaj +1 more source
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
doaj +1 more source
Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x) [PDF]
, 2012 We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer.
Miller, A. R., Paris, Richard B.
core +3 more sources
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.
core +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
openaire +3 more sources
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
doaj +1 more source
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
doaj +1 more source