Std::cyl_bessel_k,std::cyl_bessel_kf,std::cyl_bessel_kl (3) Linux Manual Page

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

Synopsis

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.

Parameters

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) =
π
2
I
-ν(x)-I
ν(x)
sin(νπ)
(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

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

// 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 = " << (pi / 2) * (std::cyl_bessel_i(-.5, x) - std::cyl_bessel_i(.5, x)) / std::sin(.5 * pi) << '\n';
}

Output:

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

External links

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

std::cyl_bessel_k,std::cyl_bessel_kf,std::cyl_bessel_kl (3) Linux Manual Page