- Type: System..::..DoubleOn entry: the argument of the function.
s13ad calculates an approximate value for .
For it is based on the Chebyshev expansion
For , where is an implementation-dependent number,
where and , .
For , to within machine precision.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
There are no failure exits from s13ad. The parameter _ifail has been included for consistency with other methods in this chapter.
If and are the relative errors in the argument and result, respectively, then in principle
The equality may hold if is greater than the machine precision ( due to data errors etc.) but if is simply due to round-off in the machine representation, then since the factor relating to is always less than one, the accuracy will be limited by machine precision.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.