Dawson
Dawson(x)
The Dawson function, or Dawson Integral, is a function defined on both real numbers and complex numbers, involving the integral of [math]\displaystyle{ e^{t^2} }[/math], but scaled by [math]\displaystyle{ e^{-x^2} }[/math] so that you don't encounter numeric overflow. It is closely related to the Erf, Faddeeva and CumNormal functions. In mathematical texts, it is often written as [math]\displaystyle{ F(x) }[/math] or [math]\displaystyle{ D_+(x) }[/math].
The Dawson function is defined as
- [math]\displaystyle{ Dawson(x) = e^{-x^2} \int_0^x e^{t^2} dt }[/math]
The [math]\displaystyle{ e^{t^2} }[/math] term appears in many mathematical and statistical contexts, but creates numeric difficulties since [math]\displaystyle{ e^{t^2} }[/math] overflows the largest double floating point when t ≥ 27. When you encounter this situation, you can often get your computation to succeed, without pushing the numeric limits, by reformulating the calculation in terms of the Dawson function.