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.
Keywords for this software
References in zbMATH (referenced in 6 articles , 1 standard article )
Showing results 1 to 6 of 6.
- Bytev, Vladimir V.; Kniehl, Bernd A.: Derivatives of any Horn-type hypergeometric functions with respect to their parameters (2020)
- Di Pietro, Lorenzo; Gaiotto, Davide; Lauria, Edoardo; Wu, Jingxiang: 3d abelian gauge theories at the boundary (2019)
- Tarasov, O. V.: Massless on-shell box integral with arbitrary powers of propagators (2018)
- Pearson, John W.; Olver, Sheehan; Porter, Mason A.: Numerical methods for the computation of the confluent and Gauss hypergeometric functions (2017)
- Frellesvig, Hjalte; Tommasini, Damiano; Wever, Christopher: On the reduction of generalized polylogarithms to (\mathrmLi_n) and (\mathrmLi_2,2) and on the evaluation thereof (2016)
- Huang, Zhi-Wei; Liu, Jueping: NumExp: numerical epsilon expansion of hypergeometric functions (2013)