NumExp swMATH ID: 16825 Software Authors: Huang, Zhi-Wei; Liu, Jueping Description: NumExp: numerical epsilon expansion of hypergeometric functions. It is demonstrated that the well-regularized hypergeometric functions can be evaluated directly and numerically. The package NumExp is presented for expanding hypergeometric functions and/or other transcendental functions in a small regularization parameter. The hypergeometric function is expressed as a Laurent series in the regularization parameter and the coefficients are evaluated numerically by using the multi-precision finite difference method. This elaborate expansion method works for a wide variety of hypergeometric functions, which are needed in the context of dimensional regularization for loop integrals. The divergent and finite parts can be extracted from the final result easily and simultaneously. In addition, there is almost no restriction on the parameters of hypergeometric functions. Homepage: http://cpc.cs.qub.ac.uk/summaries/AEPE_v1_0.html Keywords: hypergeometric functions; expansion; Feynman diagrams Related Software: Hypexp; HYPERDIRE; Mathematica; Nestedsums; XSummer; HPL; HyperInt; FastGaussQuadrature; libcwfn; Cephes; BIZ; AIZ; Algorithm 831; Matlab; CONHYP; CHAPLIN; F1; SecDec; mpmath Cited in: 6 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year NumExp: numerical epsilon expansion of hypergeometric functions. Zbl 1344.33001Huang, Zhi-Wei; Liu, Jueping 2013 all top 5 Cited by 15 Authors 1 Bytev, Vladimir V. 1 Di Pietro, Lorenzo 1 Frellesvig, Hjalte 1 Gaiotto, Davide 1 Huang, Zhiwei 1 Kniehl, Bernd A. 1 Lauria, Edoardo 1 Liu, Jueping 1 Olver, Sheehan Shakiban 1 Pearson, John W. 1 Porter, Mason Alexander 1 Tarasov, Oleg V. 1 Tommasini, Damiano 1 Wever, Christopher 1 Wu, Jingxiang Cited in 5 Serials 2 Journal of High Energy Physics 1 Computer Physics Communications 1 Nuclear Physics. B 1 Numerical Algorithms 1 Journal of Physics A: Mathematical and Theoretical Cited in 4 Fields 5 Special functions (33-XX) 3 Quantum theory (81-XX) 1 Approximations and expansions (41-XX) 1 Global analysis, analysis on manifolds (58-XX) Citations by Year