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Defined in header <cmath> | ||
| (1) | ||
float comp_ellint_2(float k); double comp_ellint_2(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) |
longdouble comp_ellint_2l(longdouble k); | (3) | (since C++17) |
Defined in header <cmath> | ||
template<class Integer> double comp_ellint_2( Integer k); | (A) | (since C++17) |
std::comp_ellint_2 for all cv-unqualified floating-point types as the type of the parameterk.(since C++23)Contents |
| k | - | elliptic modulus or eccentricity (a floating-point or integer value) |
If no errors occur, value of the complete elliptic integral of the second kind ofk, that isstd::ellint_2(k, π/2), is returned.
Errors may be reported as specified inmath_errhandling.
Implementations that do not support C++17, but supportISO 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 headertr1/cmath and namespacestd::tr1.
An implementation of this function is alsoavailable in boost.math.
The perimeter of an ellipse with eccentricityk and semimajor axisa equals4aE(k), whereE isstd::comp_ellint_2. When eccentricity equals0, the ellipse degenerates to a circle with radiusa and the perimeter equals2πa, soE(0) = π/2. When eccentricity equals1, the ellipse degenerates to a line of length 2a, whose perimeter is4a, soE(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 argumentnum of integer type,std::comp_ellint_2(num) has the same effect asstd::comp_ellint_2(static_cast<double>(num)).
#include <cmath>#include <iostream>#include <numbers> int main(){constexprdouble 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) = 1.5708π/2 = 1.5708E(1) = 1E(1, π/2) = 1
(C++17)(C++17)(C++17) | (incomplete) elliptic integral of the second kind (function)[edit] |
| Weisstein, Eric W. "Complete Elliptic Integral of the Second Kind." From MathWorld — A Wolfram Web Resource. |
