Error function

From specialfunctionswiki
Revision as of 06:54, 31 October 2014 by Tom (talk | contribs)
Jump to: navigation, search

$$\mathrm{erf}(x)=\dfrac{2}{\sqrt{\pi}}\displaystyle\int_0^x e^{-\tau^2} d\tau$$

500px

Properties

Theorem: $\mathrm{erf}(z) = \dfrac{2}{\sqrt{\pi}} \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^kz^{2n+1}}{n!(2n+1)}$

Proof:

Theorem: $\mathrm{erf}(-z)=-\mathrm{erf}(z)$

Proof:

Theorem: $\mathrm{erf}(\overline{z}) = \overline{\mathrm{erf}}(z)$

Proof: