# Expanding Gamma function around poles

by DMESONS
Tags: expanding, function, gamma, poles
 P: 27 Can someone help me to expand the following gamma functions around the pole ε, at fisrt order in ε $\Gamma[(1/2) \pm (ε/2)]$ where ε= d-4
 PF Gold P: 466 $$\Gamma(\frac{1}{2} - \frac{\epsilon}{2}) = \sqrt{\pi }+\frac{1}{2} \sqrt{\pi } \epsilon (\gamma_E +\log (4))+O\left(\epsilon ^2\right)$$ $$\Gamma(\frac{1}{2} + \frac{\epsilon}{2}) = \sqrt{\pi }+\frac{\sqrt{\pi } \epsilon \psi ^{(0)}\left(\frac{1}{2}\right)}{2}+O\left(\epsilon ^2\right)$$