Dawson function
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In mathematics, the Dawson function is
- <math>F(x) = e^{-x^2} \int_0^x e^{t^2}\,dt.<math>
The notation D(x) is also in use. The Dawson function is also called the Dawson integral.
The Dawson function is closely related to the error function erf, as
- <math> F(x) = {\sqrt{\pi} \over 2} e^{-x^2} \mathrm{erfi} (x)
= - {i \sqrt{\pi} \over 2} e^{-x^2} \mathrm{erf} (ix) <math>
where erfi is the imaginary error function, erfi(x) = − i erf(ix).
External link
- Dawson's Integral (http://mathworld.wolfram.com/DawsonsIntegral.html) (at Mathworld)