Difference between revisions of "Error function is odd"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\mathrm{erf}(-z)=-\mathrm{erf}(z),$$ wh...") |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\mathrm{erf}(-z)=-\mathrm{erf}(z),$$ | $$\mathrm{erf}(-z)=-\mathrm{erf}(z),$$ | ||
| − | where $\mathrm{erf}$ denotes the [[error function]]. | + | where $\mathrm{erf}$ denotes the [[error function]] (i.e. $\mathrm{erf}$ is an [[odd function]]). |
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
</div> | </div> | ||
</div> | </div> | ||
| + | |||
| + | ==References== | ||
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Erf of conjugate is conjugate of erf}}: 7.1.9 | ||
Revision as of 05:01, 5 June 2016
Theorem
The following formula holds: $$\mathrm{erf}(-z)=-\mathrm{erf}(z),$$ where $\mathrm{erf}$ denotes the error function (i.e. $\mathrm{erf}$ is an odd function).
Proof: █
</div>
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 7.1.9
