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

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) |

`ν`

and `x`

, is returned, that is Kν(x) =

π |

2 |

I -ν(x)-I ν(x) |

sin(νπ) |

ν(x) is

`std::cyl_bessel_i(ν,x))`

for x≥0 and non-integer ν; for integer ν a limit is used. 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.

#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

Weisstein, Eric W. "Modified Bessel Function of the Second Kind." From MathWorld--A Wolfram Web Resource.

(C++17)(C++17)(C++17) | regular modified cylindrical Bessel functions (function) |

(C++17)(C++17)(C++17) | cylindrical Bessel functions (of the first kind) (function) |

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