| Common mathematical functions | |||||||||||||||||||||||||||||||
| Mathematical special functions(C++17) | |||||||||||||||||||||||||||||||
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| C-style checked integer arithmetic | |||||||||||||||||||||||||||||||
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Defined in header <cmath> | ||
| (1) | ||
float ellint_3(float k,float nu,float phi); double ellint_3(double k,double nu,double phi); | (since C++17) (until C++23) | |
/* floating-point-type */ ellint_3(/* floating-point-type */ k, /* floating-point-type */ nu, | (since C++23) | |
float ellint_3f(float k,float nu,float phi); | (2) | (since C++17) |
longdouble ellint_3l(longdouble k,longdouble nu,longdouble phi); | (3) | (since C++17) |
Defined in header <cmath> | ||
template<class Arithmetic1,class Arithmetic2,class Arithmetic3> /* common-floating-point-type */ | (A) | (since C++17) |
std::ellint_3 for all cv-unqualified floating-point types as the type of the parametersk,nu andphi.(since C++23)Contents |
| k | - | elliptic modulus or eccentricity (a floating-point or integer value) |
| nu | - | elliptic characteristic (a floating-point or integer value) |
| phi | - | Jacobi amplitude (a floating-point or integer value, measured in radians) |
| dθ |
| (1-nusin2 θ)√1-k2 sin2 θ |
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 also available inboost.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 argumentnum1, second argumentnum2 and third argumentnum3:
| (until C++23) |
Ifnum1,num2 andnum3 have arithmetic types, thenstd::ellint_3(num1, num2, num3) has the same effect asstd::ellint_3(static_cast</* common-floating-point-type */>(num1), If no such floating-point type with the greatest rank and subrank exists, thenoverload resolution does not result in a usable candidate from the overloads provided. | (since C++23) |
#include <cmath>#include <iostream>#include <numbers> int main(){constdouble hpi=std::numbers::pi/2; std::cout<<"Π(0,0,π/2) = "<< std::ellint_3(0,0, hpi)<<'\n'<<"π/2 = "<< hpi<<'\n';}
Output:
Π(0,0,π/2) = 1.5708π/2 = 1.5708
| This section is incomplete Reason: this and other elliptic integrals deserve better examples.. perhaps calculate elliptic arc length? |
(C++17)(C++17)(C++17) | (complete) elliptic integral of the third kind (function)[edit] |
| Weisstein, Eric W. "Elliptic Integral of the Third Kind." From MathWorld — A Wolfram Web Resource. |
