Difference between revisions of "Error function"
From specialfunctionswiki
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| + | [http://www.johndcook.com/erf_and_normal_cdf.pdf Relating $\phi$ and erf] | ||
Revision as of 22:10, 13 January 2015
$$\mathrm{erf}(x)=\dfrac{2}{\sqrt{\pi}}\displaystyle\int_0^x e^{-\tau^2} d\tau$$
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: █
