Zeta and MultiZeta

07262014, 05:42 PM
Post: #1




Zeta and MultiZeta
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! 

07272014, 07:29 AM
Post: #2




RE: Zeta and MultiZeta
Zeta(x,n) is the nth derivative of the Zeta function.


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