Modern comprehensive account of the Barnes G-Function

Question

I previously put this forward on the math.stackexchange community with little luck:

I am looking for a comprehensive account of the properties and applications of the Barnes G-Function. Everything from recurrence relations, proof of the infinite product representation, functional relations, e.t.c. Ideally with proofs?

I am primarily interested only on the detailed proof of it's infinite product representation and physical applications. Other proofs are a welcomed bonus for this beauty.

Answer 1

Perhaps one of the most recent overviews of the Barnes G-function (with some new results) is Contributions to the Theory of the Barnes Function (2003). It is not a self-contained treatise, but it does contain many pointers to the literature.