In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, the Dawson function (named for John M. Dawson

John M. Dawson

John M. Dawson was an American computational physicist. He received the Aneesur Rahman prize in computational physics. The Rahman prize is the highest honor given by the American Physical Society for work in computational physics. He is credited as the inventor of the field of Plasma acceleration...

) is


The notation D(x) is also in use. The Dawson function is also called the Dawson integral

Integral

Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...

. A variation of this function is given by

The Dawson function is closely related to the error function

Error function

In mathematics, the error function is a special function of sigmoid shape which occurs in probability, statistics and partial differential equations...

erf, as


where erfi is the imaginary error function,

For |x| near zero,
and for |x| large,
More specifically, near the origin it has the series expansion


F(x) satisfies the differential equation


with the initial condition F(0) = 0.

External links

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