Matematikan, errore funtzioa honela definitzen den funtzioa da:
![{\displaystyle \operatorname {erf} (x)={\frac {2}{\sqrt {\pi }}}\int _{0}^{x}e^{-t^{2}}\,\mathrm {d} t.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9a104ff865aa73aa367d2a07c40134e4596e7726)
Taylorren garapenari esker, honela kalkula daiteke:
![{\displaystyle \operatorname {erf} (z)={\frac {2}{\sqrt {\pi }}}\sum _{n=0}^{\infty }{\frac {(-1)^{n}z^{2n+1}}{n!(2n+1)}}={\frac {2}{\sqrt {\pi }}}\left(z-{\frac {z^{3}}{3}}+{\frac {z^{5}}{10}}-{\frac {z^{7}}{42}}+{\frac {z^{9}}{216}}-\ \cdots \right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/96d20c4cfee110765dcdc02dd9278cfb8f3dd376)
Besteak beste, errore funtzioa probabilitate teorian agertzen da,
banaketa normal estandarraren banaketa funtzioa errore funtzioaren bitartez adieraz baitaiteke:
![{\displaystyle \Phi (z)={\frac {1}{2}}{\Bigl [}1+\operatorname {erf} {\Bigl (}{\frac {z}{\sqrt {2}}}{\Bigr )}{\Bigr ]},\quad x\in \mathbb {R} .}](https://wikimedia.org/api/rest_v1/media/math/render/svg/36751a284a015993eaa134753db993cb65bd1792)
Kanpo estekak