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Defined in header <cmath> | ||
| (1) | ||
float cyl_bessel_k(float nu,float x); double cyl_bessel_k(double nu,double x); | (since C++17) (until C++23) | |
/* floating-point-type */ cyl_bessel_k(/* floating-point-type */ nu, /* floating-point-type */ x); | (since C++23) | |
float cyl_bessel_kf(float nu,float x); | (2) | (since C++17) |
longdouble cyl_bessel_kl(longdouble nu,longdouble x); | (3) | (since C++17) |
Defined in header <cmath> | ||
template<class Arithmetic1,class Arithmetic2> /* common-floating-point-type */ | (A) | (since C++17) |
std::cyl_bessel_k for all cv-unqualified floating-point types as the type of the parametersnu andx.(since C++23)Contents |
| nu | - | the order of the function |
| x | - | the argument of the function |
| π |
| 2 |
| I-nu(x)-Inu(x) |
| sin(nuπ) |
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 additional overloads are not required to be provided exactly as(A). They only need to be sufficient to ensure that for their first argumentnum1 and second argumentnum2:
| (until C++23) |
Ifnum1 andnum2 have arithmetic types, thenstd::cyl_bessel_k(num1, num2) has the same effect asstd::cyl_bessel_k(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(){double pi=std::numbers::pi;constdouble x=1.2345; // spot check for nu == 0.5std::cout<<"K_.5("<< x<<") = "<< std::cyl_bessel_k(.5, x)<<'\n'<<"calculated via I = "<<(pi/2)*(std::cyl_bessel_i(-.5, x)-std::cyl_bessel_i(.5, x))/std::sin(.5* pi)<<'\n';}
Output:
K_.5(1.2345) = 0.32823calculated via I = 0.32823
(C++17)(C++17)(C++17) | regular modified cylindrical Bessel functions (function)[edit] |
(C++17)(C++17)(C++17) | cylindrical Bessel functions (of the first kind) (function)[edit] |
| Weisstein, Eric W. "Modified Bessel Function of the Second Kind." From MathWorld — A Wolfram Web Resource. |
