- #1

MatinSAR

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- Homework Statement
- Prove Residue theorem.

- Relevant Equations
- Please see the following.

Integral 7.2 is ok. I must employ the integration technique used in 7.2 to prove that integral equation 7.1 equals zero. For n<0 we have : $$\sum_{n=- \infty}^{-2} a_n \oint (z-z_0)^ndz$$For n>0 we have : $$\sum_{n=0}^{\infty} a_n \oint (z-z_0)^ndz$$

According to Cauchy's Integral Theorem, since there are no singularities within contour C, the value of the second integral is zero. But for n<0 , ##(z-z_0)^n## isn't an analytic function so it can be unzero.

How can I show that this integral is also equal to zero? Can I show it by using the substitution ##z-z_0=re^{i\theta}## like 7.2? Or I should do sth more than this...