Difference between revisions of "Error function"

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(Properties)
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=Videos=
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[https://www.youtube.com/watch?v=5v7d8jmlMi4 The Laplace transform of the error function $\mathrm{erf}(t)$]
  
 
=References=
 
=References=
 
[http://www.johndcook.com/erf_and_normal_cdf.pdf Relating $\phi$ and erf]
 
[http://www.johndcook.com/erf_and_normal_cdf.pdf Relating $\phi$ and erf]

Revision as of 02:15, 30 April 2015

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

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:

Videos

The Laplace transform of the error function $\mathrm{erf}(t)$

References

Relating $\phi$ and erf