Results 11 to 20 of about 106 (55)
Analytic continuations of the Horn $H_1$ and $H_5$ functions [PDF]
, 2023 The analytic continuations (ACs) of the double variable Horn $H_1$ and $H_5$ functions have been derived for the first time using the automated symbolic $\textit{Mathematica}$ package $\texttt{Olsson.wl}$. The use of Pfaff-Euler transformations have been
Bera, Souvik, Pathak, Tanay
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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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Certain integral representations involving hypergeometric functions in two variables [PDF]
, 2022 Various integral representations of hypergeometric functions have been introduced and investigated due to their important applications in divers fields.
Agarwal Praveen +3 more
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Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d [PDF]
, 2018 The long-standing problem of representing the general massive one-loop Feynman integral as a meromorphic function of the space-time dimension $d$ has been solved for the basis of scalar one- to four-point functions with indices one.
Phan, Khiem Hong, Riemann, Tord
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Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d [PDF]
, 2017 Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension $d$ in terms of (generalized) hypergeometric functions $_2F_1$ and $F_1$.
Bluemlein, Johannes +2 more
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On q-Horn hypergeometric functions $\mathbf{H}_6$ and $\mathbf{H}_7$
, 2021 The aim of this work is to construct various interesting properties for basic Horn functions $\mathbf{H}_6$ and $\mathbf{H}_7$ under conditions on the denominator parameters, such as several $q$-contiguous function relations, $q$-differential relations ...
Shehata, Ayman
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Specializations of partial differential equations for Feynman integrals
, 2022 Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables $z_i$, we derive a system of partial differential equations w.r.t.\ new variables $x_j$, which parameterize the differentiable ...
Bytev, Vladimir V. +2 more
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Positive Definite Functions on Complex Spheres and their Walks through Dimensions [PDF]
, 2017 We provide walks through dimensions for isotropic positive definite functions defined over complex spheres. We show that the analogues of Montée and Descente operators as proposed by Beatson and zu Castell [J. Approx.
Massa, E., Peron, A.P., Porcu, E.
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On the monodromy invariant Hermitian form for A-hypergeometric systems [PDF]
, 2020 We will give an explicit construction of the invariant Hermitian form for the monodromy of an $A$-hypergeometric system given that there is a Mellin-Barnes basis of solutions.Comment: 16 ...
Verschoor, Carlo
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, 2013 We consider A-hypergeometric functions associated to normal sets in the plane. We give a classification of all point configurations for which there exists a parameter vector such that the associated hypergeometric function is algebraic. In particular, we
Bod, Esther
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