- Thread starter
- #1

- Jan 17, 2013

- 1,667

We have the following functional equation of digamma

\(\displaystyle \psi(x+1)-\psi(x)=\frac{1}{x}\)

It is then readily seen that

\(\displaystyle \psi(x+1)-\psi(x)=\frac{1}{x}\)

It is then readily seen that

\(\displaystyle -\gamma= \lim_{z\to 0} \left\{ \psi(z) +\frac{1}{z} \right\}\)

**Prove the following**

\(\displaystyle -\gamma = \lim_{z \to 0} \left\{ \Gamma(z) -\frac{1}{z} \right\}\)

Last edited: