If a function is holomorphic in a certain domain, does it mean it necessarily has...
If a function is holomorphic in a certain domain, does it mean it necessarily has an antiderivative
Say I have a holomrphic function f(z) in domain D, say and my function is not holomorphic for - it has some poles there. Does it mean there is necessarily an antiderivative for f(z)?
I know I can use Morera's theorem and calculate all the residues inside and check if their sum is zero. However what seemed more intuitive to me is to prove that since for every contained in D, depends only on the start and end points, there exists an antiderivative for f(z).
Is my prof correct? Can I conclude that in general, a holomorphic function in a domain D not only has infinitely many derivatives in D, but it has also infinitely many antiderivatives there?