Editing Elementary function (section)

=== Non-elementary functions ===
Many mathematicians exclude non-[[Analytic function|analytic functions]] such as the [[Absolute value|absolute value function]] or discontinuous functions such as the [[step function]],<ref>{{Cite journal |last=Risch |first=Robert H. |date=1979 |title=Algebraic Properties of the Elementary Functions of Analysis |url=https://www.jstor.org/stable/2373917 |journal=American Journal of Mathematics |volume=101 |issue=4 |pages=743–759 |doi=10.2307/2373917 |jstor=2373917 |issn=0002-9327|url-access=subscription }}</ref><ref name=":0" /> but others allow them. Some have proposed extending the set to include, for example, the [[Lambert W function]].<ref>{{Cite journal |last=Stewart |first=Seán |date=2005 |title=A new elementary function for our curricula? |url=https://files.eric.ed.gov/fulltext/EJ720055.pdf |journal=Australian Senior Mathematics Journal |volume=19 |issue=2 |pages=8–26}}</ref>

Some examples of functions that are ''not'' elementary:

* [[tetration]]
* the [[gamma function]]
* non-elementary [[Liouvillian function#Examples|Liouvillian functions]], including 
** the [[exponential integral]] (''Ei''), [[logarithmic integral]] (''Li'' or ''li'') and [[Fresnel integral|Fresnel integrals]] (''S'' and ''C'').
** the [[error function]], <math>\mathrm{erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2}\,dt,</math>  a fact that may not be immediately obvious, but can be proven using the [[Risch algorithm]].
* other [[nonelementary integral]]s, including the [[Dirichlet integral]] and [[elliptic integral]].