DAWSON

Purpose:

Evaluates D(z), the Dawson Integral.

Syntax:

DAWSON(z)

Returns:

A scalar or series, the value of D(z).

Example:

dawson(1)

returns  0.538080.

Example:

dawson(1 + i)

returns 0.990373 - 0.638873i.

Example:

dawson(-10..0.01..10);

xlabel("$x$");ylabel("$D(x)$");label("Dawson Integral");

returns 2001 samples of D(x).

Example:

W1: -10..0.01..10

W2: dawson(W1)

W3: sqrt(pi)/2 * imag(faddeeva(w1))

W2 contains the Dawson integral and W3 computes the same function using the FADDEEVA function w(z).

Remarks:

The Dawson integral or Dawson function, D(z), is defined as:

or alternately:

The input z may be complex.

DAWSON uses the first definition and is computed from the FADDEEVA function based on an algorithm developed by Steven G. Johnson licensed under the MIT License. The Faddeeva function is defined as:

For real values of z, the Faddeeva function is related to the Dawson integral by:

See Also:

ERF

ERFC

ERFCINV

ERFCX

ERFI

ERFINV

FADDEEVA