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.



Modern comprehensive account of the Barnes G-Function
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](http://arxiv.org/abs/math/0308086) (2003). It is not a self-contained treatise, but it does contain many pointers to the literature.


