NAG Library Function Document
nag_dawson (s15afc) returns a value for Dawson's Integral, .
||nag_dawson (double x)
evaluates an approximation for Dawson's Integral
The function is based on two Chebyshev expansions:
, and for
. These approximations are used for those values of
for which the result is correct to machine precision
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
On entry: the argument of the function.
Error Indicators and Warnings
Let and be the relative errors in the argument and result respectively.
is considerably greater than the machine precision
is due to data errors etc.), then
are approximately related by:
The following graph shows the behaviour of the error amplification factor
However if is of the same order as machine precision, then rounding errors could make somewhat larger than the above relation indicates. In fact will be largely independent of or , but will be of the order of a few times the machine precision.
Parallelism and Performance
nag_dawson (s15afc) is not threaded in any implementation.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.
Program Text (s15afce.c)
Program Data (s15afce.d)
Program Results (s15afce.r)