Computes the Bessel functions of the first kind, \( J_{n}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+n +1)}}
{\left({x \over 2}\right)}^{2p+n }\).
It is the solution of \( x^{2}y''+xy'+(x^2-n^2)y=0\) for which \( y(0) = 0\) if \(n \ne 0\) else \(1\).
Defined in header
#include <eve/module/bessel.hpp>
{
template< eve::real_value N, eve::floating_real_value T >
}
constexpr callable_cyl_bessel_jn_ cyl_bessel_jn
Computes the Bessel functions of the first kind, .
Definition: cyl_bessel_jn.hpp:57
Definition: all_of.hpp:22
Parameters
n
: order of the function (non necessarily integral)
x
: real floating argument.
Return value
The value of \(\displaystyle J_{n}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+n +1)}}
{\left({x \over 2}\right)}^{2p+n }\) is returned.
#include <eve/module/bessel.hpp>
#include <eve/wide.hpp>
#include <iostream>
int main()
{
wide_ft x = {0.5, -1.5, 0.1, -1.0, 19.0, 25.0, 21.5, 10000.0};
wide_ft n = {0.5, 1.0, 1.5, 2.0, 2.5, 2.6, 3.2, 12};
std::cout << "---- simd" << '\n'
<< "<- n = " << n << '\n'
<< "<- x = " << x << '\n'
;
double xd = 1.0;
std::cout << "---- scalar" << '\n'
<< "<- xd = " << xd << '\n'
return 0;
}
Wrapper for SIMD registers.
Definition: wide.hpp:65