nag_dawson (s15afc) returns a value for Dawson's Integral, , via the function name.

nag_dawson (s15afc) evaluates an approximation for Dawson's Integral

The function is based on two Chebyshev expansions:

For ,

For ,

For  near zero, , and for  large, . These approximations are used for those values of  for which the result is correct to machine precision. For very large  on some machines,  may underflow and then the result is set exactly to zero (see the Users' Note for your implementation for details).

None.

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.

None.