cyl_bessel_h1

kyosu::cyl_bessel_h1 = {}

inlineconstexpr

Computes the Bessel functions of the third kind \(H^{(1)}\),.

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   template<eve::floating_scalar_value N, eve::floating_ordered_value T,>
   constexpr auto cyl_bessel_h1(N nu, T z) noexcept;
 
   template<eve::floating_scalar_value N, concepts::kyosu::complex Z>
   constexpr T    cyl_bessel_h1(N nu, Z z) noexcept;
 
   template<eve::floating_scalar_value N, eve::floating_ordered_value T, complexRange R>
   constexpr auto cyl_bessel_h1(N nu, T z, R& h1s) noexcept;
 
   template<eve::floating_scalar_value N, concepts::kyosu::complex Z, complexRange R>
   constexpr T    cyl_bessel_h1(N nu, Z z, R& h1s) noexcept;
}

Parameters

• nu: scalar floating order of the function.
• z: Value to process.
• h1s: range able to containn = int(abs(nu))+1` complex values (of type complex_t<T> or Z respectively)

Return value

• returns \(H^{(1)}_\nu(z)\).

*Ouput values

• on output (if present) h1s contains the values of \( (H^{(1)}_{\nu_0+\epsilon i})_{i = 0 \cdots n} \); where \( \nu_0 \) is the fractional part of \(\nu\) 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 = 0.0;
  std::cout << "z                    " << z << std::endl;
  for(int n=0; n <= 3; ++n)
  {
    auto h1 = kyosu::cyl_bessel_h1(v, z);
    std::cout << "v                  " << v  << std::endl;
    std::cout << "yl_bessel_h1(v, z) " << h1 << std::endl;
    v = v+0.25;
  }
  return 0;
}