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:

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