Editing Riemann zeta function (section)

===Laurent series===
The Riemann zeta function is [[meromorphic]] with a single [[pole (complex analysis)|pole]] of order one at {{math|''s'' {{=}} 1}}. It can therefore be expanded as a [[Laurent series]] about {{math|''s'' {{=}} 1}}; the series development is then<ref>{{cite journal | last1 = Hashimoto | first1 = Yasufumi | last2 = Iijima | first2 = Yasuyuki | last3 = Kurokawa | first3 = Nobushige | last4 = Wakayama | first4 = Masato | doi = 10.36045/bbms/1102689119 | issue = 4 | journal = [[Simon Stevin (journal)|Bulletin of the Belgian Mathematical Society, Simon Stevin]] | mr = 2115723 | pages = 493–516 | title = Euler's constants for the Selberg and the Dedekind zeta functions | url = https://projecteuclid.org/euclid.bbms/1102689119 | volume = 11 | year = 2004| doi-access = free }}</ref>

:<math>\zeta(s)=\frac{1}{s-1}+\sum_{n=0}^\infty \frac{\gamma_n}{n!}(1-s)^n.</math>

The constants {{math|''γ''<sub>''n''</sub>}} here are called the [[Stieltjes constants]] and can be defined by the [[limit of a sequence|limit]]

: <math> \gamma_n = \lim_{m \rightarrow \infty}{\left(\left(\sum_{k = 1}^m \frac{(\ln k)^n}{k}\right) - \frac{(\ln m)^{n+1}}{n+1}\right)}.</math>

The constant term {{math|''γ''<sub>0</sub>}} is the [[Euler–Mascheroni constant]].