DAWSON

Purpose:

Evaluates D(z), the Dawson Integral.

Syntax:

DAWSON(z)

z

-

A scalar or series, the integration limit.

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(x).

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. The Faddeeva function is defined as:

 

 

and for real z is related to the Dawson integral by:

 

See Also:

ERF

ERFC

ERFCINV

ERFCX

ERFI

ERFINV

FADDEEVA