Limit of erf when z approaches infinity and the modulus of arg(z) is less than pi/4

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.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 7.1.16