std::ellint_2, std::ellint_2f, std::ellint_2l
Defined in header <cmath>
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(1) | ||
float ellint_2 ( float k, float phi ); double ellint_2 ( double k, double phi ); |
(since C++17) (until C++23) |
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/* floating-point-type */ ellint_2( /* floating-point-type */ k, /* floating-point-type */ phi ); |
(since C++23) | |
float ellint_2f( float k, float phi ); |
(2) | (since C++17) |
long double ellint_2l( long double k, long double phi ); |
(3) | (since C++17) |
Defined in header <cmath>
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template< class Arithmetic1, class Arithmetic2 > /* common-floating-point-type */ |
(A) | (since C++17) |
std::ellint_2
for all cv-unqualified floating-point types as the type of the parameters k and phi.(since C++23)Contents |
[edit] Parameters
k | - | elliptic modulus or eccentricity (a floating-point or integer value) |
phi | - | Jacobi amplitude (a floating-point or integer value, measured in radians) |
[edit] Return value
If no errors occur, value of the incomplete elliptic integral of the second kind of k and phi, that is ∫phi
0√1-k2
sin2
θdθ, 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 |k|>1, a domain error may occur
[edit] 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 additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their first argument num1 and second argument num2:
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(until C++23) |
If num1 and num2 have arithmetic types, then std::ellint2(num1, num2) has the same effect as std::ellint2(static_cast</* common-floating-point-type */>(num1), If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the overloads provided. |
(since C++23) |
[edit] Example
#include <cmath> #include <iostream> #include <numbers> int main() { const double hpi = std::numbers::pi / 2.0; 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:
E(0,π/2) = 1.5708 E(0,-π/2) = -1.5708 π/2 = 1.5708 E(0.7,0) = 0 E(1,π/2) = 1
[edit] See also
(C++17)(C++17)(C++17) |
(complete) elliptic integral of the second kind (function) |
[edit] External links
Weisstein, Eric W. "Elliptic Integral of the Second Kind." From MathWorld — A Wolfram Web Resource. |