Behaviour of Gamma function when z = -n

[naaa00]

Hi there,

I'm actually trying to understand why the behaviour of the Gamma function at z = -n is

(-1)^n/(n!z) + O(1)

The first term (although without the z) I recognized it as the residue of f when z= -n. But the rest, no idea. Any explanation is very appreciated.

 

[Mute]

Hi there,

I'm actually trying to understand why the behaviour of the Gamma function at z = -n is

(-1)^n/(n!z) + O(1)

The first term (although without the z) I recognized it as the residue of f when z= -n. But the rest, no idea. Any explanation is very appreciated.

Where are you getting that asymptotic expression? Why does it involve both n and z? The Gamma function diverges at the negative integers; are you looking for an expansion of the Gamma function when z is close to a negative integer?