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MathsSpecial

Sine Power Integral

Evaluates the sine power integral.
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Interface

C++
Excel
HTML

Sine Power Integral

 
doublesine_power_integraldoublea
doubleb
intn )
This function evaluates the sine power integral with given parameters, defined by

The algorithm uses the fact that

Example 1

#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

References

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

Parameters

athe lower limit of integration
bthe upper limit of integration
nthe power of the sine function

Returns

An approximation of the sine power integral.

Authors

Lucian Bentea (September 2005)
Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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