# FADDEEVA

## Purpose:

Evaluates w(z), the Faddeeva function.

## Syntax:

FADDEEVA(z)

 z - A scalar or series, the integration limit.

## Returns:

A scalar or series, the value of exp(z-2) erfc(-iz).

## Example:

faddeeva(1)

returns  0.367879 + 0.607158i, the value of:

exp(-1) * erfc(-i)

## Example:

faddeeva(i)

returns 0.427584 + 0.000000i.

## Example:

faddeeva((-2..0.01..2) * i);

xlabel("x");ylabel("w(x)");label("Faddeeva Function"); returns 401 samples of w(x).

## Example:

W1: (-2..0.01..2) * i

W2: faddeeva(W1)

W3: exp(-(w1 * w1)) * erfc(-i * w1)

W2 contains the Faddeeva function and W3 computes the same function using  exp(-z2) erfc(-iz).

## Remarks:

The Faddeeva function, w(z), is defined as: The input z may be complex.

The real and imaginary parts are decomposed as: where V and L are the real and imaginary Voigt functions.

FADDEEVA is computed based on an algorithm developed by Steven G. Johnson.

The Faddeeva function is closely related to the DAWSON Integral.

DAWSON

ERF

ERFC

ERFCINV

ERFCX

ERFI

ERFINV