Editing Riemann zeta function (section)

===Rising factorial===
Another series development using the [[Pochhammer symbol|rising factorial]] valid for the entire complex plane is <ref name="Knopp"/>

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

This can be used recursively to extend the Dirichlet series definition to all complex numbers.

The Riemann zeta function also appears in a form similar to the Mellin transform in an integral over the [[Gauss–Kuzmin–Wirsing operator]] acting on {{math|''x''<sup>''s'' − 1</sup>}}; that context gives rise to a series expansion in terms of the [[falling factorial]].<ref>{{cite web|url=http://linas.org/math/poch-zeta.pdf |title=A series representation for the Riemann Zeta derived from the Gauss-Kuzmin-Wirsing Operator |website=Linas.org |access-date=2017-01-04}}</ref>