table of contents
std::sph_bessel,std::sph_besself,std::sph_bessell(3) | C++ Standard Libary | std::sph_bessel,std::sph_besself,std::sph_bessell(3) |
NAME¶
std::sph_bessel,std::sph_besself,std::sph_bessell - std::sph_bessel,std::sph_besself,std::sph_bessell
Synopsis¶
Defined in header <cmath>
double sph_bessel ( unsigned n, double x );
float sph_bessel ( unsigned n, float x );
long double sph_bessel ( unsigned n, long double x ); (1) (since
C++17)
float sph_besself( unsigned n, float x );
long double sph_bessell( unsigned n, long double x );
double sph_bessel( unsigned n, IntegralType x ); (2) (since
C++17)
1) Computes the spherical Bessel function of the first kind 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 first
kind of n and x, that is j
n(x) = (π/2x)1/2
J
n+1/2(x) where J
n(x) is std::cyl_bessel_j(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 << "j_1(" << x << ") = "
<< std::sph_bessel(1, x) << '\n';
// exact solution for j_1
std::cout << "(sin x)/x^2 - (cos x)/x = " <<
std::sin(x)/(x*x) - std::cos(x)/x << '\n';
}
Output:¶
j_1(1.2345) = 0.352106
(sin x)/x^2 - (cos x)/x = 0.352106
See also¶
cyl_bessel_j
cyl_bessel_jf
cyl_bessel_jl cylindrical Bessel functions (of the first kind)
(C++17) (function)
(C++17)
(C++17)
sph_neumann
sph_neumannf
sph_neumannl spherical Neumann functions
(C++17) (function)
(C++17)
(C++17)
External links¶
Weisstein, Eric W. "Spherical Bessel Function of the First
Kind." From MathWorld —
A Wolfram Web Resource.
2022.07.31 | http://cppreference.com |