All Questions

Reading a paper about eta invariants I came across a zeta-like function. I'm looking for the analytic continuation of $$\sum_{k=1}^\infty k(k+a)^{-s}$$ at $s=0$, where $a$ is positive. In the paper ...

For a positive sequence $0\le\lambda_{1}\le\lambda_{2}\le\cdots$, consider an infinite product \begin{equation*} \prod_{i=1}^{\infty}\lambda_{i}:=\lim_{n\rightarrow\infty}\prod_{i=1}^{n}\lambda_{i}...

For the purpose of formalisation in a theorem prover, I am looking for a simple definition of the analytic extension of the Hurwitz ζ function $\zeta(s,q)$ valid for all $s\in\mathbb{C}\setminus\{1\}$ ...