eta

auto kyosu::eta = eve::functor<eta_t>

inlineconstexpr

Computes the Dirichlet sum \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(n+1)^z}\). Sometimes this function is for obvious reasons called the alternative \(\zeta\) function .

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   template<kyosu::concepts::cayley_dickson_like T> constexpr auto eta(T z) noexcept;
}

Parameters

• z : value to process.

Return value

Returns the Dirichlet alternating zeta function: \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(n+1)^z}\)

Note

η can be used as an alias in code.

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
 
  using wide_ft = eve::wide<float, eve::fixed<4>>;
  wide_ft ref1 = {3.0f, 2.0f, 1.0f, 0.5f};
  wide_ft imf1 = {2.0f, -1.0, -5.0, 0.0};
  wide_ft ref2 = {0.0, 1.0, 2.0, 3.0};
  auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
 
  std::cout << "---- simd" << std::endl
            << "<- zc        = " << zc << std::endl
            << "-> eta(zc)   = " << kyosu::eta(zc) << std::endl
            << "-> eta(ref2)    = " << kyosu::eta(ref2) << std::endl
            << "-> η(ref2)    = " << kyosu::η(ref2) << std::endl;
 
  return 0;
}