Public Shared Function s13ac ( _ x As Double, _ <OutAttribute> ByRef ifail As Integer _ ) As Double
public: static double s13ac( double x, [OutAttribute] int% ifail )
- Type: System..::..DoubleOn entry: the argument of the function.Constraint: .
s13ac calculates an approximate value for .
For it is based on the Chebyshev expansion
For where the value of is given in the Users' Note for your implementation,
where and , .
For , to within the accuracy possible (see [Accuracy]).
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
Errors or warnings detected by the method:
- The method has been called with an argument less than or equal to zero for which the function is not defined. The result returned is zero.
If and are the absolute and relative errors in the result and is the relative error in the argument then in principle these are related by
That is accuracy will be limited by machine precision near the origin and near the zeros of , but near the zeros of only absolute accuracy can be maintained.
The behaviour of this amplification is shown in Figure 1.
For large values of , therefore and since is limited by the finite precision of the machine it becomes impossible to return results which have any relative accuracy. That is, when we have that and hence is not significantly different from zero.
Hence is chosen such that for values of , in principle would have values less than the machine precision and so is essentially zero.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.