std::comp_ellint_1,std::comp_ellint_1f,std::comp_ellint_1l(3)

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 arg );
   double comp_ellint_1( float arg );
   double comp_ellint_1( long double arg ); (1)
   float comp_ellint_1f( float arg );
   long double comp_ellint_1l( long double arg );
   double comp_ellint_1( IntegralType arg ); (2)
   1) Computes the complete elliptic integral of the first kind of arg.
   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.
   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.

Parameters
   arg - 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
   arg, that is ellint_1(arg, 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 |arg| > 1, a domain error may occur.

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.

Example
   (works as shown with gcc 6.0) // Run this code
 #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
 #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';
 }

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

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

See also
   ellint_1 (incomplete) elliptic integral of the first kind
   ellint_1f (function)
   ellint_1l