# dawson

Compute the Dawson (scaled imaginary error) function.

### Syntax

`y = dawson(z)`

### Arguments

z
vector or matrix of real or complex numbers
y
vector or matrix of real or complex numbers (of same size than x).

### Description

`dawson` computes the scaled imaginary error function, defined as

### Examples

```i = %i;
x = [0, 0.01, 1, 100, i, 2*i, 4*i, 8*i,  1-i, 1+i, 2+i, 1e-4+2e-4*i].';
[x, dawson(x), dawson(-x)]```
```--> [x, dawson(x), dawson(-x)]
ans  =
0.     + 0.i       0.        + 0.i          0.        + 0.i
0.01   + 0.i       0.0099993 + 0.i         -0.0099993 + 0.i
1.     + 0.i       0.5380795 + 0.i         -0.5380795 + 0.i
100.   + 0.i       0.0050003 + 0.i         -0.0050003 + 0.i
0.     + i         0.        + 2.0300785i   0.        - 2.0300785i
0.     + 2.i       0.        + 48.160012i   0.        - 48.160012i
0.     + 4.i       0.        + 7875110.3i   0.        - 7875110.3i
0.     + 8.i       0.        + 5.526D+27i   0.        - 5.526D+27i
1.     - i         0.9903731 + 0.6388731i  -0.9903731 - 0.6388731i
1.     + i         0.9903731 - 0.6388731i  -0.9903731 + 0.6388731i
2.     + i         0.1635394 - 0.1531246i  -0.1635394 + 0.1531246i
0.0001 + 0.0002i   0.0001    + 0.0002i     -0.0001    - 0.0002i
```

```clf
subplot(1,2,1)
x = logspace(-20,20,100);
y = dawson(x);         // the imaginary part is zero
plot("ll", x, y)
xlabel x fontsize 3
title dawson(x) fontsize 3.5
xgrid(color("grey60"))

subplot(1,2,2)
x = logspace(-7,1,100);
y = imag(dawson(x*%i)); // the real part is zero
plot("ll", x, y)
xlabel x fontsize 3
title imag(dawson(x.i)) fontsize 3.5
xgrid(color("grey60"))```

### Algorithms

This function is based on the Faddeeva package library.

• erf — fonction erreur
• erfc — fonction erreur complémentaire.
• calerf — calcule différentes fonctions d'erreur.

### History

 Version Description 5.5.0 Function dawson introduced
 Report an issue << calerf Fonctions spéciales delip >>