I'm trying to sum two indipendent random variabile, in particular two zipf's law, mathematica say that the product of two generalized harmonic number $H_{p,s}$ and $H_{t,k}$, $H_{p,s}H_{t,k}$ is eqaul to: $(\zeta(s)-\zeta(s,p+1))(\zeta(k)-\zeta(k,t+1))$ but I can't undestand how this result is possibile from the moment that I have the product of the finite sum and the $\zeta$ requires infinity sum.
Thanks.