cyl_bessel_h12

kyosu::cyl_bessel_h12 = {}

inlineconstexpr

Computes the Bessel functions of the third kind \( H^{(1)} \) and \( H^{(2)} \),.

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   template<eve::floating_scalar_value N, eve::floating_ordered_value T, complexRange R1, complexRange R2>
   constexpr auto cyl_bessel_h12(N nu, T z, R1& h1s,  R2& h2s) noexcept;
 
   template<eve::floating_scalar_value N, conceots::kyosu::complex Z, complexRange R1, complexRange R2>
   constexpr T    cyl_bessel_h12(N nu, Z z, R1& h1s,  R2& h2s) noexcept;
}

Parameters

• n: scalar floating order of the function.
• z: Value to process.
• h1s: range able to containn = int(abs(nu))+1complex values (of type complex_t<T> or Z respectively) *h2s: range able to contain n = int(abs(nu))+1 complex values (of type complex_t<T> or Z respectively)

Return value

• returns the kumi pair \( \{ H^{(1)}_\nu(z). H^{(2)}_\nu(z) \} \).

*Ouput values

• on output (if present) h1s and h2s contains the values of \( (H^{(1\|2)}_{\nu_0+\epsilon i})_{i = 0 \cdots n} \) respectively, 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 = 3.3;
  std::cout << "z                    " << z << std::endl;
  std::vector<decltype(z)> h1(4), h2(4);
  kyosu::cyl_bessel_h12(v, z, h1, h2);
  for(int n=0; n <= 3; ++n)
  {
    std::cout << "h1[" << n << "] = " << h1[n] << std::endl;
    std::cout << "h2[" << n << "] = " << h2[n] << std::endl;
  }
  return 0;
}