std::sph_neumann, std::sph_neumannf, std::sph_neumannl
Defined in header <cmath>
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(1) | ||
float sph_neumann ( unsigned n, float x ); double sph_neumann ( unsigned n, double x ); |
(since C++17) (until C++23) |
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/* floating-point-type */ sph_neumann( unsigned n, /* floating-point-type */ x ); |
(since C++23) | |
float sph_neumannf( unsigned n, float x ); |
(2) | (since C++17) |
long double sph_neumannl( unsigned n, long double x ); |
(3) | (since C++17) |
Defined in header <cmath>
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template< class Integer > double sph_neumann ( unsigned n, Integer x ); |
(A) | (since C++17) |
std::sph_neumann
for all cv-unqualified floating-point types as the type of the parameter x.(since C++23)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 nn(x) = (π/2x)1/2
Nn+1/2(x) where Nn(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.
The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::sph_neumann(int_num, num) has the same effect as std::sph_neumann(int_num, static_cast<double>(num)).
[edit] Example
Output:
n_1(1.2345) = -0.981201 -cos(x)/x² - sin(x)/x = -0.981201
[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) |
[edit] External links
Weisstein, Eric W. "Spherical Bessel Function of the Second Kind." From MathWorld — A Wolfram Web Resource. |