User:Jdforrester (WMF)/Test formulae

The following infinite series converges for all complex numbers s with real part greater than 1, and defines ζ(s) in this case:



\zeta(s) = \sum_{n=1}^\infty n^{-s} = \frac{1}{1^s} + \frac{1}{2^s} + \frac{1}{3^s} + \cdots \;\;\;\;\;\;\; \sigma = \mathfrak{R}(s) > 1. \!$$