std::ellint_2, std::ellint_2f, std::ellint_2l
double ellint_2( double k, double φ ); float ellint_2f( float k, float φ ); |
(1) | (since C++17) |
Promoted ellint_2( Arithmetic k, Arithmetic φ ); |
(2) | (since C++17) |
Promoted
is also long double, otherwise the return type is always double.Parameters
k | - | elliptic modulus or eccentricity (a value of a floating-point or integral type) |
φ | - | Jacobi amplitude (a value of floating-point or integral type, measured in radians) |
Return value
If no errors occur, value of the incomplete elliptic integral of the second kind of k
and φ
, that is ∫φ
0√1-k2
sin2
θdθ, 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
Example
#include <cmath> #include <iostream> int main() { double hpi = std::acos(-1)/2; std::cout << "E(0,π/2) = " << std::ellint_2(0, hpi) << '\n' << "E(0,-π/2) = " << std::ellint_2(0, -hpi) << '\n' << "π/2 = " << hpi << '\n' << "E(0.7,0) = " << std::ellint_2(0.7, 0) << '\n' << "E(1,π/2) = " << std::ellint_2(1, hpi) << '\n'; }
Output:
F(0,π/2) = 1.5708 F(0,-π/2) = -1.5708 π/2 = 1.5708 F(0.7,0) = 0 E(1,π/2) = 1
External links
Weisstein, Eric W. "Elliptic Integral of the Second Kind." From MathWorld--A Wolfram Web Resource.
See also
(C++17)(C++17)(C++17) |
(complete) elliptic integral of the second kind (function) |