NAG Library Function Document

nag_sin_integral (s13adc)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

nag_sin_integral (s13adc) returns the value of the sine integral
Six=0xsinuudu,  
.

2
Specification

#include <nag.h>
#include <nags.h>
double  nag_sin_integral (double x)

3
Description

nag_sin_integral (s13adc) calculates an approximate value for Six.
For x16.0 it is based on the Chebyshev expansion
Six=xr=0arTrt,t=2 x16 2-1.  
For 16<x<xhi, where xhi is an implementation-dependent number,
Six=signx π2-fxcosxx-gxsinxx2  
where fx=r=0frTrt and gx=r=0grTrt, t=2 16x 2-1.
For xxhi, Six=12π signx to within machine precision.

4
References

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

5
Arguments

1:     x doubleInput
On entry: the argument x of the function.

6
Error Indicators and Warnings

None.

7
Accuracy

If δ and ε are the relative errors in the argument and result, respectively, then in principle
ε δ sinx Six .  
The equality may hold if δ is greater than the machine precision (δ due to data errors etc.) but if δ is simply due to round-off in the machine representation, then since the factor relating δ to ε is always less than one, the accuracy will be limited by machine precision.

8
Parallelism and Performance

nag_sin_integral (s13adc) is not threaded in any implementation.

9
Further Comments

None.

10
Example

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

10.1
Program Text

Program Text (s13adce.c)

10.2
Program Data

Program Data (s13adce.d)

10.3
Program Results

Program Results (s13adce.r)

GnuplotProduced by GNUPLOT 4.6 patchlevel 3 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −10 −5 0 5 10 Si(x) x Example Program Returned Values for the Sine Integral Si(x) gnuplot_plot_1
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017