NAG CL Interface
s15afc (dawson)

1 Purpose

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

2 Specification

#include <nag.h>
double  s15afc (double x)
The function may be called by the names: s15afc, nag_specfun_dawson or nag_dawson.

3 Description

s15afc evaluates an approximation for Dawson's Integral
Fx = e-x2 0x et2 dt .  
The function is based on two Chebyshev expansions:
For 0<x4,
Fx = x r=0 ar Tr t ,   where   t=2 x4 2 -1 .  
For x>4,
Fx = 1x r=0 br Tr t ,   where   t=2 4x 2 -1 .  
For x near zero, Fxx, and for x large, Fx12x. These approximations are used for those values of x for which the result is correct to machine precision.

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

1: x double Input
On entry: the argument x of the function.

6 Error Indicators and Warnings


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

s15afc is not threaded in any implementation.

9 Further Comments


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)