Higuys, I'm having a bit of trouble showing this.
Any help is much appreciated
$\displaystyle \displaystyle(\frac{1}{2i\pi})\oint_{C} (\frac{e^{tz}}{z^{n+1}}) dz = \frac{t^n}{n!} $
where C is the unit circle |z|=1
Higuys, I'm having a bit of trouble showing this.
Any help is much appreciated
$\displaystyle \displaystyle(\frac{1}{2i\pi})\oint_{C} (\frac{e^{tz}}{z^{n+1}}) dz = \frac{t^n}{n!} $
where C is the unit circle |z|=1
$\displaystyle
\displaystyle
e^{tz}=\sum \ \frac{t^nz^n}{n!}
$
n term is only non zero:
$\displaystyle \displaystyle
(\frac{1}{2i\pi})\oint_{C} ( \ \frac{t^nz^n}{n!} \frac{1}{z^{n+1}}) dz =(\frac{1}{2i\pi}) \ \ \frac{t^n}{n!} \oint_{C} \frac{dz}{z}}= \frac{t^n}{n!}
$