nag_sin_integral (s13adc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG Library Manual

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:     xdoubleInput
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

Not applicable.

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)

Produced by GNUPLOT 4.4 patchlevel 0 -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)

nag_sin_integral (s13adc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014