cyl_bessel_j0

kyosu::cyl_bessel_j0 = {}

inlineconstexpr

Computes the Bessel function of the first kind, \( J_0(x)=\frac1{\pi }\int _{0}^{\pi}\cos(x\sin \tau) \,\mathrm {d} \tau \) extended to the complex plane and cayley_dickson algebras.

It is the solution of \( x^{2}y''+xy'+x^2y=0\) for which \( y(0) = 1\).

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_j0(T z) noexcept;
   template<eve::floating_ordered_value T>     constexpr T    cyl_bessel_j0(T z) noexcept;
}

Parameters

• z: Value to process.

Return value

• returns \(J_0(z)\).

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
  using kyosu::cyl_bessel_j0;
  std::cout.precision(16);
 
  std::cout << "1.0   " << " -> " << cyl_bessel_j0(1.0) << "\n";
  std::cout << "1+0i  " << " -> " << cyl_bessel_j0(kyosu::complex(1.0, 0.0)) << "\n";
  std::cout << "15.0  " << " -> " << cyl_bessel_j0(15.0) << "\n";
  std::cout << "15+0i " << " -> " << cyl_bessel_j0(kyosu::complex(15.0, 0.0)) << "\n";
  std::cout << "40.0  " << " -> " << cyl_bessel_j0(40.0) << "\n";
  std::cout << "40+0i " << " -> " << cyl_bessel_j0(kyosu::complex(40.0, 0.0)) << "\n";
  std::cout << "60.0  " << " -> " << cyl_bessel_j0(60.0) << "\n";
  std::cout << "60+0i " << " -> " << cyl_bessel_j0(kyosu::complex(60.0, 0.0)) << "\n";
 
  eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
  auto zz = kyosu::complex(z);
  std::cout << z << " -> \n" << cyl_bessel_j0(z) << "\n";
  std::cout << zz << " -> \n" << cyl_bessel_j0(zz) << "\n";
 
  std::cout << "1.0                 " << " -> " << cyl_bessel_j0(1.0) << "\n";
  std::cout << "1.0+36.0i           " << " -> " << cyl_bessel_j0(kyosu::complex(1.0, 36.0)) << "\n";
  std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << cyl_bessel_j0(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
 
 
  eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0),  z2(36.0, 0.5, 0.0, 40.0);
  auto z0 = kyosu::complex(z1, z2);
  std::cout << z0 << "\n -> " << cyl_bessel_j0(z0) << "\n";
 
  eve::wide<double, eve::fixed<8>> l(1.0, 15.0, 40.0, 60.0, eve::inf(eve::as<double>()),eve::minf(eve::as<double>()), eve::nan(eve::as<double>()), 0.0);
  auto lims = kyosu::complex(l);
  std::cout << lims << " -> \n" << cyl_bessel_j0(lims) << "\n";
  std::cout << l    << " -> \n" << cyl_bessel_j0(l)    << "\n";
  auto nanan = kyosu::complex(eve::nan(eve::as<double>()), eve::nan(eve::as<double>()));
  std::cout << nanan << " -> \n" << cyl_bessel_j0(nanan) << std::endl;
 
  return 0;
}