I need to show that the property of being a domain of holomorphy is the same as being a holomorphically convex domain (this result is known as Cartan-Thullen theorem). However, the proofs I found in textbooks (e.g. Shabat) look ugly and are hard to digest.


Is there a reference with a better proof? Can you share your intuition on looking at this result? Thanks in advance.



Characterization of a domain of holomorphy
I can't really anticipate what you will find ugly and hard to digest, but at least I found the proof in Jiří Lebls book "Tasty Bits of Several Complex Variables", Theorem 2.6.3, to be nicely presented (but I don't think it is very different from what is found in many other sources).


In general, I think this book is a very friendly introduction to basic results in SCV like this, and it is freely available at
<https://www.jirka.org/scv/>


