std::sph_neumann, std::sph_neumannf, std::sph_neumannl
| double sph_neumann ( unsigned n, double x ); double sph_neumann ( unsigned n, float x ); |
(1) | (since C++17) |
| double sph_neumann( unsigned n, Integral x ); |
(2) | (since C++17) |
n and x.Contents |
[edit] Parameters
| n | - | the order of the function |
| x | - | the argument of the function |
[edit] 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
[edit] 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
[edit] 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
[edit] Example
Output:
n_1(1.2345) = -0.981201 -(cos x)/x^2 - (sin x)/x = -0.981201
[edit] External links
Weisstein, Eric W. "Spherical Bessel Function of the Second Kind." From MathWorld--A Wolfram Web Resource.
[edit] See also
| (C++17)(C++17)(C++17) |
cylindrical Neumann functions (function) |
| (C++17)(C++17)(C++17) |
spherical Bessel functions (of the first kind) (function) |