Fast formulas for the Hurwitz values $\zeta (2,a)$ and $\zeta (3,a)$

We prove two fast formulas for the Hurwitz values $\zeta (2,a)$ and $\zeta (3,a)$ respectively with the help of the WZ method. In them $(a{)}_n$ denotes the rising factorial or Pochhammer’s symbol defined by $(a{)}_0=1$ and $(a{)}_n=a(a+1)\cdots (a+n-1)$ for positive integers $n$. The Huwitz $\zeta$ function is defined by $\zeta (s,a)=\zeta (0,s,a)={\sum }_{k=0}^{\mathrm{\infty }}(k+a{)}^{-s}$. In addition, we can use these fast evaluations to compute also in a rapid way Dirichlet values of the kinds $L_{\chi }(2)$ and $L_{\chi }(3)$.