A Unifying Integral Representation of the Gamma Function and Its Reciprocal

Peter Reinhard Hansen, Chen Tong

We derive an integral expression $G(z)$ for the reciprocal gamma function, $1/\hat{I}“(z)=G(z)/\ddot{I}€$, that is valid for all $z\in \mathbb{C}$, without the need for analytic continuation. Th…