Mathematical methods in physics

Question

How to solve $\Gamma(-n)$? Which formula is good to get answer for the above question? I tried of various formulae to solve it but I couldn't make it out. What is the right way to approach the above question?

Answer 1

Euler's reflection formula for $\Gamma(z)$ is what you want. $$ \Gamma(-z) = \frac{-\pi}{\sin(\pi z)\Gamma(1+z)} $$ From this formula it is clear to see that for even integers $\Gamma(n)$ is $\infty$ or undefined and for odd integers it is $\frac{\pm\pi}{\Gamma(n+1)}$. Hope this helps.

Edit: As some have pointed out im an idiot. Eulers reflection formula is undefined for integers.