Zeta and MultiZeta

[Alberto Candel]

The Prime has the Zeta function (\(\zeta\)) in the ToolBox->Math->Special->Zeta. It is defined for real \(s>1\) by \(\zeta(s) =\displaystyle{ \sum_{n=1}^\infty \dfrac{1}{n^{s}}}\).

When doing some calculations I obtain expressions involving \(\zeta(s,t)\). What are these? They do not seem to be the multizetas. For example, the multizeta \[\zeta(2,1) = \sum_{n=1}^\infty \dfrac{1+1/2+1/3+\cdots+1/n}{(n+1)^2} = \sum_{n=1}^\infty \dfrac{1}{n^3} = \zeta(3),\]
but the Prime gives the approximate value \(\zeta(2,1)=-0.937548254316\), while Apery's constant \(\zeta(3)=1.20205690316\).

Thanks!

[parisse]

Zeta(x,n) is the n-th derivative of the Zeta function.