The Cauchy-Goursat Theorem states:(adsbygoogle = window.adsbygoogle || []).push({});

Let ##f## be holomorphic in asimply connected domain D. If C is a simple closed contour that lies in D, then

##\int_C f(z) \mathrm{d}t = 0 ##

Now if ##f## is holo just on ##|C| \bigcup \ int(C)## (i.e ##f## holo only on the contour and inside of it, if we take ##z_0 \in \mathbb{C}## can we deduce from the theorem that

## \int_C \frac{f'(z)}{z-z_0} \mathrm{d}t = \int_C \frac{f(z)}{(z-z_0)^2} \mathrm{d}t = 0 ## whether ##z_0 \in \left[\ |C| \bigcup \ int(C) \right]## ornot

Since both equal ##0##.

Also where does ##z## must belong to for the theorem to apply?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The Cauchy-Goursat Theorem

**Physics Forums | Science Articles, Homework Help, Discussion**