Dawson function

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 (at Mathworld)