std::cyl_bessel_k,std::cyl_bessel_kf,std::cyl_bessel_kl (3) - Linux Manuals

std::cyl_bessel_k,std::cyl_bessel_kf,std::cyl_bessel_kl: std::cyl_bessel_k,std::cyl_bessel_kf,std::cyl_bessel_kl


std::cyl_bessel_k,std::cyl_bessel_kf,std::cyl_bessel_kl - std::cyl_bessel_k,std::cyl_bessel_kf,std::cyl_bessel_kl


double cyl_bessel_k( double ν, double x );
float cyl_bessel_kf( float ν, float x ); (1) (since C++17)
long double cyl_bessel_kl( long double ν, long double x );
Promoted cyl_bessel_k( Arithmetic ν, Arithmetic x ); (2) (since C++17)

1) Computes the irregular_modified_cylindrical_Bessel_function (also known as modified Bessel function of the second kind) of ν and x.
2) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by (1). If any argument has integral_type, it is cast to double. If any argument is long double, then the return type Promoted is also long double, otherwise the return type is always double.


ν- the order of the function
x - the argument of the function)

Return value

If no errors occur, value of the irregular modified cylindrical Bessel function (modified Bessel function of the second kind) of ν and x, is returned, that is K
ν(x) =



(where I
ν(x) is std::cyl_bessel_i(ν,x)) for x≥0 and non-integer ν; for integer ν a limit is used.

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 ν>=128, the behavior is implementation-defined


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


// Run this code

  #include <cmath>
  #include <iostream>
  int main()
      double pi = std::acos(-1);
      double x = 1.2345;

      // spot check for ν == 0.5
      std::cout << "K_.5(" << x << ") = " << std::cyl_bessel_k( .5, x) << '\n'
                << "calculated via I = " <<
                       -std::cyl_bessel_i(.5,x))/std::sin(.5*pi) << '\n';


  K_.5(1.2345) = 0.32823
  calculated via I = 0.32823

External links

Weisstein,_Eric_W._"Modified_Bessel_Function_of_the_Second_Kind." From MathWorld--A Wolfram Web Resource.

See also

cyl_bessel_il regular modified cylindrical Bessel functions

cyl_bessel_jl cylindrical Bessel functions (of the first kind)