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.