std::cyl_neumann,std::cyl_neumannf,std::cyl_neumannl (3) - Linux Manuals

std::cyl_neumann,std::cyl_neumannf,std::cyl_neumannl: std::cyl_neumann,std::cyl_neumannf,std::cyl_neumannl

NAME

std::cyl_neumann,std::cyl_neumannf,std::cyl_neumannl - std::cyl_neumann,std::cyl_neumannf,std::cyl_neumannl

Synopsis

double cyl_neumann( double ν, double x );
float cyl_neumannf( float ν, float x ); (1) (since C++17)
long double cyl_neumannl( long double ν, long double x );
Promoted cyl_neumann( Arithmetic ν, Arithmetic x ); (2) (since C++17)

1) Computes the cylindrical_Neumann_function (also known as Bessel function of the second kind or Weber function) 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 cylindrical Neumann function (Bessel function of the second kind) of ν and x, is returned, that is N
ν(x) =

J
ν(x)cos(νπ)-J
-ν(x)
sin(νπ)

(where J
ν(x) is std::cyl_bessel_j(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 << "N_.5(" << x << ") = " << std::cyl_neumann(.5, x) << '\n'
                << "calculated via J = " <<
                (std::cyl_bessel_j(.5,x)*std::cos(.5*pi)
               - std::cyl_bessel_j(-.5,x))/std::sin(.5*pi) << '\n';
  }

Output:

  N_.5(1.2345) = -0.236973
  calculated via J = -0.236973

External links

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