NAG Library Function Document

nag_dawson (s15afc)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

nag_dawson (s15afc) returns a value for Dawson's Integral, Fx.

2
Specification

#include <nag.h>
#include <nags.h>
double  nag_dawson (double x)

3
Description

nag_dawson (s15afc) evaluates an approximation for Dawson's Integral
Fx=e-x20xet2dt.  
The function is based on two Chebyshev expansions:
For 0<x4,
Fx=xr=0arTrt,   where  t=2 x4 2-1.  
For x>4,
Fx=1xr=0brTrt,   where  t=2 4x 2-1.  
For x near zero, Fxx, and for x large, Fx 12x . These approximations are used for those values of x for which the result is correct to machine precision.

4
References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

5
Arguments

1:     x doubleInput
On entry: the argument x of the function.

6
Error Indicators and Warnings

None.

7
Accuracy

Let δ and ε be the relative errors in the argument and result respectively.
If δ is considerably greater than the machine precision (i.e., if δ is due to data errors etc.), then ε and δ are approximately related by:
ε x 1-2xFx Fx δ.  
The following graph shows the behaviour of the error amplification factor x 1-2xFx Fx :
Figure 1
Figure 1
However if δ is of the same order as machine precision, then rounding errors could make ε somewhat larger than the above relation indicates. In fact ε will be largely independent of x or δ, but will be of the order of a few times the machine precision.

8
Parallelism and Performance

nag_dawson (s15afc) is not threaded in any implementation.

9
Further Comments

None.

10
Example

This example reads values of the argument x from a file, evaluates the function at each value of x and prints the results.

10.1
Program Text

Program Text (s15afce.c)

10.2
Program Data

Program Data (s15afce.d)

10.3
Program Results

Program Results (s15afce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017