On \(q\)-analogues of the Barnes multiple zeta functions (Q2372712)

The authors introduce \(q\)-analogues of the Barnes multiple zeta functions \[ \zeta_ r(s,z)=\sum_ {n_ 1,\dots ,n_ r\geq0}(n_ 1+\cdots+n_ r+z)^ {-s}. \] They prove that these functions can be extended meromorphically to the whole plane, and moreover, tend to the Barnes multiple zeta functions when \(q\neq 1\) for all complex numbers.