Computes the modified Bessel function of the second kind, \( K_1(x)=\int_{0}^{\infty} e^{-x \cosh \tau} \cosh \tau\,\mathrm{d}\tau\).
It is a solution of \( x^{2}y''+xy'-(1+x^2)y=0\) for which \( y(0) = \infty\).
Defined in header
#include <eve/module/bessel.hpp>
{
template< eve::floating_real_value T >
}
constexpr callable_cyl_bessel_k1_ cyl_bessel_k1
Computes the modified Bessel function of the second kind, .
Definition: cyl_bessel_k1.hpp:53
Definition: all_of.hpp:22
Parameters
x
: positive real floating argument.
Return value
The value of \( \displaystyle K_1(x)=\int_{0}^{\infty} e^{-x \cosh \tau}
\cosh \tau\,\mathrm{d}\tau\) is returned.
#include <eve/module/bessel.hpp>
#include <eve/wide.hpp>
#include <iostream>
int main()
{
wide_ft pf = {0.5, 1.5, 0.1, 1.0, 19.0, 25.0, 21.5, 10000.0};
std::cout << "---- simd" << '\n'
<< "<- pf = " << pf << '\n'
;
double xd = 1.0;
std::cout << "---- scalar" << '\n'
<< "<- xd = " << xd << '\n'
return 0;
}
Wrapper for SIMD registers.
Definition: wide.hpp:65