std::sph_neumann,std::sph_neumannf,std::sph_neumannl (3) - Linux Manuals

std::sph_neumann,std::sph_neumannf,std::sph_neumannl: std::sph_neumann,std::sph_neumannf,std::sph_neumannl


std::sph_neumann,std::sph_neumannf,std::sph_neumannl - std::sph_neumann,std::sph_neumannf,std::sph_neumannl


double sph_neumann ( unsigned n, double x );
float sph_neumann ( unsigned n, float x );
long double sph_neumann ( unsigned n, long double x ); (1) (since C++17)
float sph_neumannf( unsigned n, float x );
long double sph_neumannl( unsigned n, long double x );
double sph_neumann( unsigned n, IntegralType x ); (2) (since C++17)

1) Computes the spherical_Bessel_function_of_the_second_kind, also known as the spherical Neumann function, of n and x.
2) A set of overloads or a function template accepting an argument of any integral_type. Equivalent to (1) after casting the argument to double.


n - the order of the function
x - the argument of the function

Return value

If no errors occur, returns the value of the spherical Bessel function of the second kind (spherical Neumann function) of n and x, that is n
n(x) = (π/2x)1/2
n+1/2(x) where N
n(x) is std::cyl_neumann(n,x) and x≥0

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 n>=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()
      // spot check for n == 1
      double x = 1.2345;
      std::cout << "n_1(" << x << ") = " << std::sph_neumann(1, x) << '\n';

      // exact solution for n_1
      std::cout << "-(cos x)/x^2 - (sin x)/x = "
                << -std::cos(x)/(x*x) - std::sin(x)/x << '\n';


  n_1(1.2345) = -0.981201
  -(cos x)/x^2 - (sin x)/x = -0.981201

External links

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

See also

cyl_neumannl cylindrical Neumann functions

sph_bessell spherical Bessel functions (of the first kind)