  Let $x$ be a complex number which has a positive real part, and
$w_1,\ldots,w_N$ be positive rational numbers. We show that $w^s \zeta_N (s, x
\ |\ w_1,\ldots, w_N)$ can be expressed as a finite linear combination of the
Hurwitz zeta functions over $\mathbb Q(x)$, where $\zeta_N (s,x \ |\
w_1,\ldots, w_N)$ is the Barnes zeta function and $w$ is a positive rational
number explicitly determined by $w_1,\ldots, w_N$. Furthermore, we give
generalizations of Kummer's formula on the gamma function and Koyama-Kurokawa's
formulae on the multiple gamma functions, and an explicit formula for the
values at non-positive integers for higher order derivatives of the Barnes zeta
function in the case that $x$ is a positive rational number, involving the
generalized Stieltjes constants and the values at positive integers of the
Riemann zeta function. Our formulae also makes it possible to calculate an
approximation in the case that $w_1, \ldots, w_N$ and $x$ are positive real
numbers.
