Category:Examples of Use of Reciprocal times Derivative of Gamma Function

This category contains examples of use of Reciprocal times Derivative of Gamma Function.

Let $z \in \C \setminus \Z_{\le 0}$.

Then:

$\ds \dfrac {\map {\Gamma'} z} {\map \Gamma z} = -\gamma + \sum_{n \mathop = 1}^\infty \paren {\frac 1 n - \frac 1 {z + n - 1} }$

where:

$\map \Gamma z$ denotes the Gamma function

$\map {\Gamma'} z$ denotes the derivative of the Gamma function

$\gamma$ denotes the Euler-Mascheroni constant.