std::sph_bessel,std::sph_besself,std::sph_bessell (3) - Linux Manuals

std::sph_bessel,std::sph_besself,std::sph_bessell: std::sph_bessel,std::sph_besself,std::sph_bessell

NAME

std::sph_bessel,std::sph_besself,std::sph_bessell - std::sph_bessel,std::sph_besself,std::sph_bessell

Synopsis

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

External links

Weisstein,_Eric_W._"Spherical_Bessel_Function_of_the_First_Kind." From MathWorld--A Wolfram Web Resource.