It's mean first derivative for first variable.
\!\(\*SuperscriptBox[\(Zeta\),
TagBox[
RowBox[{"(",
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[-2, 3/2] // InputForm
(*Derivative[1, 0][Zeta][-2, 3/2]*)
You can write it like this:
Limit[D[Zeta[x, 3/2], x], x -> -2]
% // FunctionExpand
(*-(Log[2]/4) + (3 Zeta[3])/(16 \[Pi]^2)*)
%//N
(*-0.15045*)
