Reciprocal gamma function

Summary

The reciprocal gamma function is the function $z \mapsto 1/\Gamma(z)$, where $\Gamma$ is the gamma function. Because $\Gamma$ has no zeros and only simple poles at $0, -1, -2, \ldots$, the reciprocal is an entire function with simple zeros exactly at these points. It is often more convenient than $\Gamma$ itself: it has an everywhere convergent Weierstrass product and a Hankel contour integral valid for all $z$.