Zeta and MultiZeta - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: HP Prime (/forum-5.html) +--- Thread: Zeta and MultiZeta (/thread-1878.html) |
Zeta and MultiZeta - Alberto Candel - 07-26-2014 05:42 PM 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! RE: Zeta and MultiZeta - parisse - 07-27-2014 07:29 AM Zeta(x,n) is the n-th derivative of the Zeta function. |