`dawson`

Dawson integral.

Category: Mathematics > Mathematical Functions

Syntax

Y = dawson(X)

Evaluates F(x) = exp(-x^2) * integral from 0 to x of exp(t^2) dt.

Description

The Dawson function is an odd function with a single maximum, about 0.541 near x = 0.924, and decays like 1/(2x) for large x. It is linked to the imaginary error function by dawson(x) = sqrt(pi)/2 * exp(-x^2) * erfi(x).

Input arguments

X: Numeric array.

Output arguments

Y: Array of the same size.

Example

Values and the erfi relation

x = [0 0.5 2];
dawson(x)
sqrt(pi)/2 * exp(-x.^2) .* erfi(x)

Output

ans = 1×3

         0    0.4244    0.3013
ans = 1×3

         0    0.4244    0.3013

See also

erfi erf erfc fresnelc