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

 

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Mathematical special functions

assoc_laguerreassoc_laguerrefassoc_laguerrel assoc_legendreassoc_legendrefassoc_legendrel betabetafbetal comp_ellint_1comp_ellint_1fcomp_ellint_1l comp_ellint_2comp_ellint_2fcomp_ellint_2l comp_ellint_3comp_ellint_3fcomp_ellint_3l cyl_bessel_icyl_bessel_ifcyl_bessel_il

cyl_bessel_jcyl_bessel_jfcyl_bessel_jl cyl_bessel_kcyl_bessel_kfcyl_bessel_kl cyl_neumanncyl_neumannfcyl_neumannl ellint_1ellint_1fellint_1l ellint_2ellint_2fellint_2l ellint_3ellint_3fellint_3l expintexpintfexpintl

hermitehermitefhermitel laguerrelaguerreflaguerrel legendrelegendreflegendrel riemann_zetariemann_zetafriemann_zetal sph_besselsph_besselfsph_bessell sph_legendresph_legendrefsph_legendrel sph_neumannsph_neumannfsph_neumannl

 

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 );	(1)
double      comp_ellint_3( IntegralType k, IntegralType nu );	(2)

1) Computes the complete elliptic integral of the third 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_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.

Parameters

nu	-	value of a floating-point or integral type
k	-	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_3(k, nu, 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 either |k| > 1 or |nu| > 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 << "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';
}

Output:

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

External links

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

See also

ellint_3ellint_3fellint_3l

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