NumExp：超几何函数的数值展开
NumExp: Numerical epsilon expansion of hypergeometric functions
摘要：
证明了正则化超几何函数可以直接数值计算。NumExp是一个用于在小正则化参数下展开超几何函数和/或其他超越函数的软件包。将超几何函数表示为正则化参数的Laurent级数，并利用多精度有限差分法对系数进行数值计算。这种精细的展开方法适用于各种各样的超几何函数，这些函数在循环积分的维度正则化的背景下是需要的。发散部分和有限部分可以很容易地从最终结果中同时提取出来。此外，对超几何函数的参数几乎没有限制。
英文摘要：
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.
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