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

double      comp_ellint_1( double arg );

double      comp_ellint_1( float arg );
double      comp_ellint_1( long double arg );
float       comp_ellint_1f( float arg );

long double comp_ellint_1l( long double arg );
double      comp_ellint_1( Integral arg );
4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to (1) after casting the argument to double.

As all special functions, comp_ellint_1 is only guaranteed to be available in <cmath> 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.


[edit] Parameters

arg - value of a floating-point or integral type

[edit] Return value

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

[edit] 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 |arg|>1, a domain error may occur

[edit] Notes

Implementations that do not support TR 29124 but support TR 19768, provide this function in the header tr1/cmath and namespace std::tr1

An implementation of this function is also available in boost.math

[edit] Example

(works as shown with gcc 6.0)

#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';


K(0) = 1.5708
π/2 = 1.5708
K(0.5) = 1.68575
F(0.5, π/2) = 1.68575

[edit] External links

Weisstein, Eric W. "Complete Elliptic Integral of the First Kind." From MathWorld--A Wolfram Web Resource.

[edit] See also

(incomplete) elliptic integral of the first kind
(function) [edit]