Dawson function - Citizendia

The Dawson function,

D + (x)

, around the origin

The Dawson function,

D - (x)

, around the origin

In mathematics, the Dawson function is

$F(x) = e^{-x^2} \int_0^x e^{t^2}\,dt.$

The notation D(x) is also in use. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and The Dawson function is also called the Dawson integral. The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space

The Dawson function is closely related to the error function erf, as

$F(x) = {\sqrt{\pi} \over 2} e^{-x^2} \mathrm{erfi} (x) = - {i \sqrt{\pi} \over 2} e^{-x^2} \mathrm{erf} (ix)$

where erfi is the imaginary error function, erfi(x) = − i erf(ix). In Mathematics, the error function (also called the Gauss error function) is a Special function (non- elementary) which occurs in Probability

For |x| near zero, $F(x)\approx x$ , and for |x| large, $F(x)\approx \frac{1}{2x}$ .

F(x) satisfies the differential equation

$\frac{dF}{dx} + 2xF=1$

with the initial condition F(0)=0.

External links

Cephes - C and C++ language special functions math library
Dawson's Integral (at Mathworld)

This mathematical analysis-related article is a stub. Analysis has its beginnings in the rigorous formulation of Calculus. You can help Wikipedia by expanding it.

© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
network: | |