Computes the Bessel functions of the second kind, \( Y_{n}(x)=\frac{2(z/2)^{-n}}{\sqrt\pi\, \Gamma(1/2-n)}\int _{1}^{\infty}\frac{\cos x\tau}
{(\tau^2-1)^{n+1/2}}\,\mathrm {d} \tau \).
It is a solution of \( x^{2}y''+xy'+(x^2-n^2)y=0\) for which \( y(0) = \infty\).
Defined in header
#include <eve/module/bessel.hpp>
{
template< eve::real_value N, eve::floating_real_value T >
}
constexpr callable_cyl_bessel_yn_ cyl_bessel_yn
Computes the Bessel functions of the second kind, .
Definition: cyl_bessel_yn.hpp:57
Definition: all_of.hpp:22
Parameters
Return value
The value of \(\displaystyle Y_{n}(x)=\frac{2(z/2)^{-n}}{\sqrt\pi\,
\Gamma(1/2-n)}\int _{1}^{\infty}\frac{\cos x\tau}{(\tau^2-1)^{n+1/2}}\,\mathrm {d} \tau \) 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