std::comp_ellint_2, std::comp_ellint_2f, std::comp_ellint_2l

From cppreference.com
Technical specifications
Filesystem library (filesystem TS)
Library fundamentals (library fundamentals TS)
Library fundamentals 2 (library fundamentals 2 TS)
Extensions for parallelism (parallelism TS)
Extensions for parallelism 2 (parallelism TS v2)
Extensions for concurrency (concurrency TS)
Concepts (concepts TS)
Ranges (ranges TS)
Special mathematical functions (special math TR)
double comp_ellint_2( double arg );

double comp_ellint_2( float arg );
double comp_ellint_2( long double arg );
float comp_ellint_2f( float arg );

long double comp_ellint_2l( long double arg );
(1)
double comp_ellint_2( IntegralType arg );
(2)
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_2 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 second kind of arg, that is ellint_2(arg,/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)

#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
#include <cmath>
#include <iostream>
int main()
{
    double hpi = std::acos(-1)/2;
    std::cout << "E(0) = " << std::comp_ellint_2(0) << '\n'
              << "/2 = " << hpi << '\n'
              << "E(0.5) = " << std::comp_ellint_2(0.5) << '\n'
              << "E(0.5, /2) = " << std::ellint_2(0.5, hpi) << '\n';
}

Output:

E(0) = 1.5708
/2 = 1.5708
E(0.5) = 1.46746
E(0.5, /2) = 1.46746

External links

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

See also

(incomplete) elliptic integral of the second kind
(function)