Difference between revisions of "Taylor series for error function"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\mathrm{erf}(z) = \dfrac{2}{...") |
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<strong>[[Taylor series for error function|Theorem]]:</strong> The following formula holds: | <strong>[[Taylor series for error function|Theorem]]:</strong> The following formula holds: | ||
$$\mathrm{erf}(z) = \dfrac{2}{\sqrt{\pi}} \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^kz^{2k+1}}{k!(2k+1)},$$ | $$\mathrm{erf}(z) = \dfrac{2}{\sqrt{\pi}} \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^kz^{2k+1}}{k!(2k+1)},$$ | ||
| − | where $\mathrm{erf}$ denotes the [[error function]] and $\pi$ denotes [[pi]]. | + | where $\mathrm{erf}$ denotes the [[error function]] and $\pi$ denotes [[pi]], and $k!$ denotes the [[factorial]]. |
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
</div> | </div> | ||
</div> | </div> | ||
Revision as of 17:24, 23 May 2016
Theorem: The following formula holds: $$\mathrm{erf}(z) = \dfrac{2}{\sqrt{\pi}} \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^kz^{2k+1}}{k!(2k+1)},$$ where $\mathrm{erf}$ denotes the error function and $\pi$ denotes pi, and $k!$ denotes the factorial.
Proof: █
