beta

kyosu::beta = {}

inlineconstexpr

Computes the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\) for real or complex entries.

Defined in Header

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   auto beta(auto x, auto y) noexcept;
}

Parameters

• x,y : Values to process. Can be a mix of cayley_dickson and real floating values.

Return value

1. If x and y are real typed values returns \(\displaystyle \mathbf{B}(x,y) = \int_0^1 t^{x-1}(1-t)^{y-1}\mbox{d}t\)
2. \(\displaystyle \mathbf{B}(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\) is returned.

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
  using kyosu::beta;
  using kyosu::complex_t;
  using e_t = float;
  using c_t = kyosu::complex_t<float>;
  using we_t = eve::wide<float, eve::fixed<2>>;
  using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
 
  std::cout << "Real:        "<< "\n";
  e_t e0(1);
  e_t e1(2);
  std::cout << e0 << ", " << e1 << " -> "  << beta(e0, e1) << "\n";
  std::cout << e0 << ", " << e0 << " -> "  << beta(e0, e0) << "\n";
  we_t we0(e0);
  we_t we1(e1);
  std::cout << we0 << ", " << we1 << " -> " << beta(we0, we1) << "\n";
 
  std::cout << "Complex:     "<< "\n";
  c_t c0(1, 5);
  c_t c1(5, 9);
  std::cout << c0 << ", " << c1 << " -> "  << beta(c0, c1) << "\n";
  std::cout << c0 << ", " << c0 << " -> "  << beta(c0, c0) << "\n";
  wc_t wc0(c0, c1);
  wc_t wc1(c1, c1);
  std::cout << wc0 << ", " << wc1 << " -> " << beta(wc0, wc1) << "\n";
 
  return 0;
}