NAME

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

Synopsis

Defined in header <cmath>
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.

Parameters

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
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

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()
{
// 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)/x² - (sin x)/x = "
<< -std::cos(x)/(x*x) - std::sin(x)/x << '\n';
}

Output:

n_1(1.2345) = -0.981201
-(cos x)/x² - (sin x)/x = -0.981201

See also

cyl_neumann
cyl_neumannf
cyl_neumannl cylindrical Neumann functions
(C++17) (function)
(C++17)
(C++17)
sph_bessel
sph_besself
sph_bessell spherical Bessel functions (of the first kind)
(C++17) (function)
(C++17)
(C++17)

External links

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