# Computing Reciprocal Gamma

Reciprocal Gamma $1/\Gamma(z)$ is an entire function and so it has a convergent Taylor series expansion which was given in its wikipedia article.

http://en.wikipedia.org/wiki/Reciprocal_gamma_function

The problem is there is no citation for it so I want to ask where I can find a proof/derivation of its power series expansion?

• It follows easily from the expansion for $\ln\Gamma$ which in turn is immediately derived from the infinite product for $\Gamma$, as explained in several references at the end of the Wikipedia article. – მამუკა ჯიბლაძე Jun 21 '14 at 2:51

$$\frac{1}{\Gamma(z)} = z + \gamma z^2 + \left(\frac{\gamma^2}{2} - \frac{\pi^2}{12}\right)z^3 + \cdots,$$
is as much of the Taylor series as is known, since closed forms of $\zeta(n)$ are only known for he even integers $n$. See here for a recursive formula for the coefficients of the Gamma function's reciprocal.