MHB Problems for Cauchy Integral Formula

shirokuma
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Hello everyone!
I am currently stuck at the two type of questions below, because I am not really sure what method should be used to calculate these question...
Could you give me a hint how to do these questions? :(
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Welcome, Shirokuma!

Consider using partial fraction decomposition. You might need to use Cauchy's differentiation formula at some points.
 
I posted this question on math-stackexchange but apparently I asked something stupid and I was downvoted. I still don't have an answer to my question so I hope someone in here can help me or at least explain me why I am asking something stupid. I started studying Complex Analysis and came upon the following theorem which is a direct consequence of the Cauchy-Goursat theorem: Let ##f:D\to\mathbb{C}## be an anlytic function over a simply connected region ##D##. If ##a## and ##z## are part of...

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