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

C++

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Special mathematical functions

assoc_laguerreassoc_laguerrefassoc_laguerrel assoc_legendreassoc_legendrefassoc_legendrel betabetafbetal comp_ellint_1comp_ellint_1fcomp_ellint_1l comp_ellint_2comp_ellint_2fcomp_ellint_2l comp_ellint_3comp_ellint_3fcomp_ellint_3l cyl_bessel_icyl_bessel_ifcyl_bessel_il

cyl_bessel_jcyl_bessel_jfcyl_bessel_jl cyl_bessel_kcyl_bessel_kfcyl_bessel_kl cyl_neumanncyl_neumannfcyl_neumannl ellint_1ellint_1fellint_1l ellint_2ellint_2fellint_2l ellint_3ellint_3fellint_3l expintexpintfexpintl

hermitehermitefhermitel laguerrelaguerreflaguerrel legendrelegendreflegendrel riemann_zetariemann_zetafriemann_zetal sph_besselsph_besselfsph_bessell sph_legendresph_legendrefsph_legendrel sph_neumannsph_neumannfsph_neumannl

double sph_neumann ( unsigned n, double x ); double sph_neumann ( unsigned n, float x ); double sph_neumann ( unsigned n, long double x ); float sph_neumannf( unsigned n, float x ); long double sph_neumannl( unsigned n, long double x );	(1)	(since C++17)
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) = (/2x)1/2
N
n+1/2(x) where N
n(x) is std::cyl_neumann(n,x) and x0

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)/x^2 - (sin x)/x = "
              << -std::cos(x)/(x*x) - std::sin(x)/x << '\n';
}

Output:

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_neumanncyl_neumannfcyl_neumannl (C++17)(C++17)(C++17)	cylindrical Neumann functions (function)
sph_besselsph_besselfsph_bessell (C++17)(C++17)(C++17)	spherical Bessel functions (of the first kind) (function)