I cannot understand the following statement in the proof of Lemma 8.7 in "Lectures on Riemann Surfaces" by Otto Forster.

whereQuote:

Since the integral depends holomorphically on , the function is holomorphic on .

are holomorphic functions on .

In the equation

the integrand can be written as where is holomorphic with respect to , to prove to be holomorphic, it seems enough to show that is continuous with respenct to . But, I don't know how to show it.

Any help would be appreciated.

Thanks in advance.