I'm studying the Casimir Effect with perfect spherical boundary which involves the use of the Hurwitz zeta function. I've been staring for a while at this equation:

\begin{align} \sum_{l=1}^{\infty}\left(l+1/2\right)^0=\sum_{l=1}^{\infty}\frac{1}{\left(l+1/2\right)^0}-1=\zeta(0,1/2)-1 \end{align}

But I can't understand the first step. Where does that $-1$ come from?


Observe that the Hurwitz zeta function is given by $$ \zeta(z,q):=\sum_{n=0}^{\infty}\frac{1}{\left(n+q\right)^z} $$ The index starts at $0$. It explains formally why you have $-1$.

  • $\begingroup$ I feel so dumb... Thanks! $\endgroup$ – ignacio.d.t Apr 22 at 17:56

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.