In Griffiths and Harris, Principles of Algebraic Geometry, on page 8, near the end of the proof of the Weierstrass Preparation Theorem, he states that $h(z,w)$ has only removable singularities in the disk $|w| < r$ and writes the cauchy integral formula and states that this implies that $h(z,w)$ is holomorphic in z as well. I don't understand how the above follows?
He does a similar thing in the proof of Hartog's extension theorem on page 7, writing the Cauchy integral formula and claims that $\frac{\partial}{\partial \bar{z_{1}}}f = 0$ which I don't find obvious.
Could someone please explain this? I feel that this should be fairly obvious but I can't seem to see the above.
Does anyone know a good reference for this book that would contain a more detailed treatment of complex analysis that Griffiths&Harris talks about? This seems to be the only background material I'm not familiar with.
Thanks!