On values of the higher derivatives of the Barnes zeta function at non-positive integers

Shinpei Sakane, Miho Aoki

Let $x$ be a complex number which has a positive real part, and $w_1,\dots ,w_N$ be positive rational numbers. We show that $w^s{\zeta }_N(s,x|w_1,\dots ,w_N)$ can be expressed a…