- Type: System..::..DoubleOn entry: the argument of the function.
s15af evaluates an approximation for Dawson's Integral
The method is based on two Chebyshev expansions:
For near zero, , and for large, . 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
Let and be the relative errors in the argument and result respectively.
If is considerably greater than the machine precision (i.e., if is due to data errors etc.), then and 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.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.