On the Barnes Function

The multiple Barnes function, defined as a generalization of the Euler gamma function, is used in many applications of pure and applied mathematics and theoretical physics. This paper presents new integral representations, asymptotic series and some special values of the Barnes function of the rational argument. Moreover, the Barnes function is expressed in a closed form by means of the Hurwitz zeta function. These results can be used for numeric and symbolic computations of the Barnes function.