Evaluates the sine power integral.

Contents

Interface Function Documentation Page Comments

Interface

#include <codecogs/maths/special/sine_power_integral.h>

using namespace Maths::Special;

	double	sine_power_integral (double a, double b, int n) Evaluates the sine power integral.
	Real	cc_sine_power_integral (Real a, Real b, Integer n) This function is available as a Microsoft Excel add-in.

Function Documentation

This function evaluates the sine power integral with given parameters, defined by

The algorithm uses the fact that

Example:

#include <codecogs/maths/special/sine_power_integral.h>
#include <iostream>
#include <iomanip>
 
int main()
{
  std::cout << std::setprecision(10);
  std::cout << "For lower and upper bounds a = 0 and b = 10, " << std::endl;
  std::cout << "and 0 <= n < 10, the value of the integral is" << std::endl;
  for (int n = 0; n < 10; n++)
  {
    std::cout << "n = " << n << " : ";
    std::cout << Maths::Special::sine_power_integral(0, 10, n) << std::endl;
  }
  return 0;
}

Output:

For lower and upper bounds a = 0 and b = 10,
and 0 <= n < 10, the value of the integral is
n = 0 : 10
n = 1 : 1.839071529
n = 2 : 4.771763687
n = 3 : 1.308824601
n = 4 : 3.545048474
n = 5 : 1.061758823
n = 6 : 2.947543192
n = 7 : 0.913186379
n = 8 : 2.577621119
n = 9 : 0.8124365163

Parameters:

a	the lower limit of integration
b	the upper limit of integration
n	the power of the sine function

Returns:

An approximation of the sine power integral.

References:

John Burkardt's library of statistical C++ routines, http://www.csit.fsu.edu/~burkardt/cpp_src/prob/prob.html

Authors:

Lucian Bentea (September 2005)