Asymptotic behavior of Sievert integral

Theorem

The following formula holds: $$S(x,\theta) \sim \sqrt{ \dfrac{\pi}{2x} } e^{-x} \mathrm{erf} \left( \sqrt{\dfrac{x}{2}} \theta \right),$$ where $S$ denotes the Sievert integral, $\pi$ denotes pi, $e^{-x}$ denotes the exponential, and $\mathrm{erf}$ denotes the error function.

References

1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $27.4.1$