Reciprocal gamma written as an infinite product

Theorem

The following formula holds: $$\dfrac{1}{\Gamma(z)} = ze^{\gamma z} \displaystyle\prod_{k=1}^{\infty} \left( 1 + \dfrac{z}{k}\right)e^{-\frac{z}{k}},$$ where $\dfrac{1}{\Gamma}$ is the reciprocal gamma function, and $\gamma$ is the Euler-Mascheroni constant.

References

• 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): §1.1 (3)