Contour Integral Representation
An integral representation due to Hermann Hankel is
where C is a path encircling 0 in the positive direction, beginning at and returning to positive infinity with respect for the branch cut along the positive real axis. According to Schmelzer & Trefethen, numerical evaluation of Hankel's integral is the basis of some of the best methods for computing the gamma function.
Read more about this topic: Reciprocal Gamma Function
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