Gamma functions

• Aug 8th 2009, 04:20 AM
grahamlee
Gamma functions
Could somone help me to solve the following gamma function:

T(2+i)/T(-2+i)

Thank you
• Aug 8th 2009, 05:55 AM
chisigma
May be You find useful the following expression of $\Gamma(*)$ as 'infinite product'...

$\Gamma (z) = \frac {e^{-\gamma z}}{z} \prod_{n=1}^{\infty} \frac{e^{\frac{z}{n}}}{1+\frac{z}{n}}$

Kind regards

$\chi$ $\sigma$
• Aug 9th 2009, 11:52 AM
Texxy
Use the recursion relation $\Gamma(z+1)=z\Gamma(z)$. Then $\frac{\Gamma(2+i)}{\Gamma(-2+i)}=\frac{i(1+i)(-1+i)(-2+i)\Gamma(i)}{\Gamma(i)}=2+4i$.