NAG Library Function Document

nag_sin_integral (s13adc)

nag_sin_integral (s13adc) returns the value of the sine integral $\mathrm{Si}\left(x\right)$.

nag_sin_integral (s13adc) evaluates

The approximation is based on several Chebyshev expansions.

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

None.

If $\delta$ and $\epsilon$ are the relative errors in the argument and result, respectively, then in principle $\left|\epsilon \right|\simeq \left|\left(\delta \sin x\right)/\mathrm{Si}\left(x\right)\right|$. 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.

For $\left|x\right|\ge x_{\mathrm{hi}}$, where $x_{\mathrm{hi}}$ is a machine-dependent value, $\mathrm{Si}\left(x\right)=\frac{1}{2}\pi \mathrm{sign}x$ to within machine precision.

None.

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