std::comp_ellint_1,std::comp_ellint_1f,std::comp_ellint_1l (3) - Linux Manuals

std::comp_ellint_1,std::comp_ellint_1f,std::comp_ellint_1l: std::comp_ellint_1,std::comp_ellint_1f,std::comp_ellint_1l

NAME

std::comp_ellint_1,std::comp_ellint_1f,std::comp_ellint_1l - std::comp_ellint_1,std::comp_ellint_1f,std::comp_ellint_1l

Synopsis

double comp_ellint_1( double k );
float comp_ellint_1( float k );
long double comp_ellint_1( long double k ); (1) (since C++17)
float comp_ellint_1f( float k );
long double comp_ellint_1l( long double k );
double comp_ellint_1( IntegralType k ); (2) (since C++17)

1) Computes the complete_elliptic_integral_of_the_first_kind of k.
2) A set of overloads or a function template accepting an argument of any integral_type. Equivalent to (1) after casting the argument to double.

Parameters

k - elliptic modulus or eccentricity (a value of a floating-point or integral type)

Return value

If no errors occur, value of the complete elliptic integral of the first kind of k, that is ellint_1(k,π/2), is returned.

Error handling

Errors may be reported as specified in math_errhandling

* If the argument is NaN, NaN is returned and domain error is not reported
* If |k|>1, a domain error may occur

Notes

Implementations that do not support C++17, but support ISO_29124:2010, provide this function if __STDCPP_MATH_SPEC_FUNCS__ is defined by the implementation to a value at least 201003L and if the user defines __STDCPP_WANT_MATH_SPEC_FUNCS__ before including any standard library headers.
Implementations that do not support ISO 29124:2010 but support TR 19768:2007 (TR1), provide this function in the header tr1/cmath and namespace std::tr1
An implementation of this function is also available_in_boost.math
The period_of_a_pendulum of length l, given acceleration due to gravity g, and initial angle θ equals 4
√
l/gK(sin2
(θ/2)), where K is std::comp_ellint_1.

Example

// Run this code

  #include <cmath>
  #include <iostream>
  int main()
  {
      double hpi = std::acos(-1)/2;
      std::cout << "K(0) = " << std::comp_ellint_1(0) << '\n'
                << "π/2 = " << hpi << '\n'
                << "K(0.5) = " << std::comp_ellint_1(0.5) << '\n'
                << "F(0.5, π/2) = " << std::ellint_1(0.5, hpi) << '\n';
      std::cout << "Period of a pendulum length 1 m at 90 degree initial angle is "
                << 4*std::sqrt(1/9.80665)*
                   std::comp_ellint_1(std::pow(std::sin(hpi/2),2)) << " s\n";
  }

Output:

  K(0) = 1.5708
  π/2 = 1.5708
  K(0.5) = 1.68575
  F(0.5, π/2) = 1.68575
  Period of a pendulum length 1 m at 90 degree initial angle is 2.15324 s

External links

Weisstein,_Eric_W._"Complete_Elliptic_Integral_of_the_First_Kind." From MathWorld--A Wolfram Web Resource.