public static double s13ad(
	double x
)

Public Shared Function s13ad ( _
	x As Double _
) As Double

public:
static double s13ad(
	double x
)

static member s13ad : 
        x : float -> float 

s13ad returns the value of the sine integral .

s13ad calculates an approximate value for $\mathrm{Si}\left(x\right)$.

For $\left|x\right|\le 16.0$ it is based on the Chebyshev expansion For $16<\left|x\right|<x_{\mathrm{hi}}$, where $x_{\mathrm{hi}}$ is an implementation-dependent number, where $f\left(x\right)={\displaystyle \underset{r=0}{{\sum }^{\prime }}}{f}_r{T}_r\left(t\right)$ and $g\left(x\right)={\displaystyle \underset{r=0}{{\sum }^{\prime }}}{g}_r{T}_r\left(t\right)$, $t=2{\left(\frac{16}{x}\right)}^2-1$.

For $\left|x\right|\ge x_{\mathrm{hi}}$, $\mathrm{Si}\left(x\right)=\frac{1}{2}\pi \mathrm{sign} x$ 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 $\delta$ and $\epsilon$ are the relative errors in the argument and result, respectively, then in principle The equality may hold if $\delta$ is greater than the machine precision ($\delta$ due to data errors etc.) but if $\delta$ is simply due to round-off in the machine representation, then since the factor relating $\delta$ to $\epsilon$ is always less than one, the accuracy will be limited by machine precision.

None.

None.

This example reads values of the argument $x$ from a file, evaluates the function at each value of $x$ and prints the results.