std::comp_ellint_3, std::comp_ellint_3f, std::comp_ellint_3l

Technical specifications
Filesystem library (filesystem TS)
Library fundamentals (library fundamentals TS)
Library fundamentals 2 (library fundamentals TS v2)
Library fundamentals 3 (library fundamentals TS v3)
Extensions for parallelism (parallelism TS)
Extensions for parallelism 2 (parallelism TS v2)
Extensions for concurrency (concurrency TS)
Concepts (concepts TS)
Ranges (ranges TS)
Mathematical special functions (special functions TR)
double      comp_ellint_3( double k, double nu );

float       comp_ellint_3( float k, float nu );
long double comp_ellint_3( long double k, long double nu );
float       comp_ellint_3f( float k, float nu );

long double comp_ellint_3l( long double k, long double nu );
double      comp_ellint_3( IntegralType k, IntegralType nu );
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_3 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

nu - value of a floating-point or integral type
k - value of a floating-point or integral type

[edit] Return value

If no errors occur, value of the complete elliptic integral of the second kind of arg, that is ellint_3(k,nu,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 either |k|>1 or |nu|>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 << "Π(0, 0.75) = " << std::comp_ellint_3(0, 0.75) << '\n'
              << "π/2 = " << hpi << '\n'
              << "Π(0.5, 0.75) = " << std::comp_ellint_3(0.5, 0.75) << '\n'
              << "Π(0.5, 0.75, π/2) = " << std::ellint_3(0.5, 0.75, hpi) << '\n';


Π(0, 0.75) = 3.14159
π/2 = 1.5708
Π(0.5, 0.75) = 3.45372
Π(0.5, 0.75, π/2) = 3.45372

[edit] External links

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

[edit] See also

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