nag_dawson (s15afc) (PDF version)
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s Chapter Introduction
NAG C Library Manual

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. For very large x on some machines, Fx may underflow and then the result is set exactly to zero (see the Users' Note for your implementation for details).

4  References

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

5  Arguments

1:     xdoubleInput
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  Further Comments

None.

9  Example

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

9.1  Program Text

Program Text (s15afce.c)

9.2  Program Data

Program Data (s15afce.d)

9.3  Program Results

Program Results (s15afce.r)


nag_dawson (s15afc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012