Difference between revisions of "Limit of erf when z approaches infinity and the modulus of arg(z) is less than pi/4"
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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Continued fraction for 1/sqrt(pi) integral from -infinity to infinity of e^(-t^2)/(z-t) dt|next=}}: 7.1.16 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Continued fraction for 1/sqrt(pi) integral from -infinity to infinity of e^(-t^2)/(z-t) dt|next=findme}}: 7.1.16 |
[[Category:Theorem]] | [[Category:Theorem]] | ||
Latest revision as of 02:18, 6 June 2016
Theorem
The following formula holds for $\left|\mathrm{arg}(z)\right| < \dfrac{\pi}{4}$ where $\mathrm{arg}(z)$ denotes the argument of $z$: $$\displaystyle\lim_{z \rightarrow \infty} \mathrm{erf}(z)=1,$$ where $\mathrm{erf}$ denotes the error function.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 7.1.16
