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

 

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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

 

Defined in header <cmath>
	(1)
float       comp_ellint_2 ( float k ); double      comp_ellint_2 ( double k ); long double comp_ellint_2 ( long double k );			(since C++17) (until C++23)
/* floating-point-type */ comp_ellint_2( /* floating-point-type */ k );			(since C++23)
float       comp_ellint_2f( float k );		(2)	(since C++17)
long double comp_ellint_2l( long double k );		(3)	(since C++17)
Additional overloads
Defined in header <cmath>
template< class Integer > double      comp_ellint_2 ( Integer k );		(A)	(since C++17)

1-3) Computes the complete elliptic integral of the second kind of k. The library provides overloads of std::comp_ellint_2 for all cv-unqualified floating-point types as the type of the parameter k. (since C++23)

A) Additional overloads are provided for all integer types, which are treated as double.

Parameters

k

-

elliptic modulus or eccentricity (a floating-point or integer value)

Return value

If no errors occur, value of the complete elliptic integral of the second kind of k, that is std::ellint_2(k, 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 |k|>1, a domain error may occur.

Notes

Implementations that do not support C++17, but support ISO 29124:2010, provide this function 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.

Implementations that do not support ISO 29124:2010 but support TR 19768:2007 (TR1), provide this function in the header tr1/cmath and namespace std::tr1.

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

The perimeter of an ellipse with eccentricity k and semimajor axis a equals 4aE(k), where E is std::comp_ellint_2. When eccentricity equals 0, the ellipse degenerates to a circle with radius a and the perimeter equals 2πa, so E(0) = π/2. When eccentricity equals 1, the ellipse degenerates to a line of length 2a, whose perimeter is 4a, so E(1) = 1.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::comp_ellint_2(num) has the same effect as std::comp_ellint_2(static_cast<double>(num)).

Example

Run this code

#include <cmath>
#include <iostream>
#include <numbers>
 
int main()
{
    constexpr double hpi = std::numbers::pi / 2.0;
 
    std::cout << "E(0) = " << std::comp_ellint_2(0) << '\n'
              << "π/2 = " << hpi << '\n'
              << "E(1) = " << std::comp_ellint_2(1) << '\n'
              << "E(1, π/2) = " << std::ellint_2(1, hpi) << '\n';
}

Output:

E(0) = 1.5708
π/2 = 1.5708
E(1) = 1
E(1, π/2) = 1

See also

ellint_2ellint_2fellint_2l (C++17)(C++17)(C++17)

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

External links

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