Cauchy's differintegral formula

1. Mar 30, 2014

Jhenrique

The Cauchy's differintegral formula is: $$\frac{d^n}{dz^n}f(z_0)=\frac{n!}{2\pi i!}\oint_{\gamma}\frac{f(z)}{(z-z_0)^{n+1}}dz$$ But this formula is valid if the derivative is wrt $\bar{z}$ ? $$\frac{d^n}{d\bar{z}^n}f(z_0)$$ And if the integral is wrt $\bar{z}$ is valid too? $$\frac{n!}{2\pi i!}\oint_{\gamma}\frac{f(z)}{(z-z_0)^{n+1}}d\bar{z}$$

2. Mar 31, 2014

micromass

Staff Emeritus
Try to prove it!

3. Mar 31, 2014

Jhenrique

I'm not capable to prove it!