# multiplication formula for gamma function

For any integer $n>0$, the gamma function satisfes the following relation:

 $\Gamma(nz)=(2\pi)^{n-1\over 2}n^{nz-{1\over 2}}\prod\limits_{k=0}^{n-1}\Gamma% \left(z+{k\over n}\right)$

This equation is true for all complex values of $z$ for which both sides are defined.

Title multiplication formula for gamma function MultiplicationFormulaForGammaFunction 2013-03-22 14:44:08 2013-03-22 14:44:08 rspuzio (6075) rspuzio (6075) 8 rspuzio (6075) Theorem msc 33B15 msc 30D30