arXiv subjects

B. Kniehl

Publications and source records attributed to B. Kniehl.

5 recordsLinked to original sources

arXiv2017

Derivatives of Horn-type hypergeometric functions with respect to their parameters

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 the same variables and with the same region of convergence as for original Horn function. The derivatives of Appell functions, generalized hypergeometric functions, confluent and non-confluent Lauricella series and generalized Lauricella series are explicitly presented. Applications to the calculation of Feynman diagrams are discussed, especially the series expansion in $ε$ within dimensional regularization. Connections with other classes of special functions are discussed as well.

math-ph↗

arXiv2016

HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalizedhypergeometric functions: Fc hypergeometric function of three variables

We present a further extension of the HYPERDIRE project, which is devoted to the creation of a set of Mathematica-based program packages for manipulations with Horn-type hypergeometric functions on the basis of differential equations. Specifically, we present the implementation of the differential reduction for the Lauricella function $F_C$ of three variables.

math-ph↗

arXiv2013

HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4

HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: one, pfq, is relevant for manipulations of hypergeometric functions_{p+1}F_p, and the second one, AppellF1F4, for manipulations with Appell hypergeometric functions F_1,F_2,F_3,F_4 of two variables.

math-ph↗

arXiv2008

Heavy quark pair production in gluon fusion at next-to-next-to-leading ${\cal O}(α_s^4)$ order: One-loop squared contributions

We calculate the next-to-next-to-leading order ${\cal O}(α_s^4)$ one-loop squared corrections to the production of heavy-quark pairs in the gluon-gluon fusion process. Together with the previously derived results on the $q \bar{q}$ production channel the results of this paper complete the calculation of the one-loop squared contributions of the next-to-next-to-leading order ${\cal O}(α_s^4)$ radiative QCD corrections to the hadroproduction of heavy flavors. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in dimensional regularization.

hep-ph↗

arXiv1998

A critical phenomenological study of inclusive photon production in hadronic collisions

We discuss fixed target and ISR inclusive photon production and attempt a comparison between theory and experiments. The dependence of the theoretical predictions on the structure functions, and on the renormalization and factorization scales is investigated. The main result of this study is that the data cannot be simultaneously fitted with a single set of scales and structure functions. On the other hand, there is no need for an additional intrinsic $k_{_T}$ to force the agreement between QCD predictions and experiments, with the possible exception of one data set. Since the data cover almost overlapping kinematical ranges this raises the question of consistency among data sets. A comparative discussion of some possible sources of experimental uncertainties is sketched.

hep-ph↗