cyl_bessel_kn

kyosu::cyl_bessel_kn = {}

inlineconstexpr

Computes the modified Bessel functions of the second kind, \( K_{n}(x)=\lim_{\alpha\to n}{\frac {\pi }{2}}{\frac {I_{-\alpha }(x)-I_{\alpha }(x)}{\sin \alpha \pi }}\). extended to the complex plane and cayley_dickson algebras.

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_kn(int n, T z) noexcept;
   template<eve::floating_ordered_value T>     constexpr T    cyl_bessel_kn(int n, T z) noexcept;
}

Parameters

• z: Value to process.

Return value

• returns \(K_n(z)\).

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
  std::cout.precision(16);
  using w_t = eve::wide<double, eve::fixed<2>>;
  auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
   for(int n=2; n <= 10; ++n)
   {
     auto kn = kyosu::cyl_bessel_kn(n, z);
     std::cout << "n " << n  << ", z " << z << std::endl;
     std::cout << "cyl_bessel_kn(n, z) " << kn << std::endl;
  }
  return 0;
}