NumExp: Numerical epsilon expansion of hypergeometric functions

Understand

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.