cyl_bessel_ik

kyosu::cyl_bessel_ik = {}

inlineconstexpr

Computes the modified Bessel functions \(I\) and \(K\),.

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   template<eve::floating_scalar_ordered_value N, eve::floating_ordered_value T, complexRange R>
   constexpr auto cyl_bessel_ik(N nu, T z, R& js,  R& ys) noexcept;
 
   template<eve::floating_scalar_ordered_value N, conceots::kyosu::complex Z, complexRange R>
   constexpr T    cyl_bessel_ik(N n, Z z, R& js,  R& ys) noexcept;
}

Parameters

• nu: scalar order of the function not necessarily integral.
• z: Value to process.
• js: range able to contain int(nu)+1 complex values (of type complex_t<T> or Z respectively) *ys: range able to contain int(nu)+1 complex values (of type complex_t<T> or Z respectively)

Return value

• returns the kumi pair \(\{I_\nu(z), K_\nu(z)\}\) of complex values.

*Ouput values

• on output js contains the values of \(((I_{\nu_0+\epsilon i})_{i = 0\cdot n}\)

• on output ys contains the values of \(((K_{\nu_0+\epsilon i})_{i = 0\cdot n}\)

  where \(\nu_0\) is the fractional part of \(\nu\), \(\nu = \nu_0+\epsilon n\) and \(\epsilon\) is the sign of \(\nu\) .

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));
  auto v = 3.3;
  std::cout << "z                    " << z << std::endl;
  std::vector<kyosu::complex_t<w_t>> is(4), ks(4);
  kyosu::cyl_bessel_ik(v, z, is, ks);
  for(int n=0; n <= 3; ++n)
  {
    std::cout << "is[" << n << "] = " << is[n] << std::endl;
    std::cout << "ks[" << n << "] = " << ks[n] << std::endl;
  }
  return 0;
}