Difference between revisions of "Asymptotic behavior of Sievert integral"
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(Created page with "==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 ...") |
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| − | {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev= | + | {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Relationship between Sievert integral and exponential integral E}}: $27.4.1$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
Revision as of 01:59, 21 December 2016
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.
Proof
References
1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $27.4.1$
