zeta

auto kyosu::zeta = eve::functor<zeta_t>

inlineconstexpr

Computes the Riemann \( \displaystyle\zeta(z)=\sum_0^\infty \frac{1}{(n+1)^z}\).

Header file

#include <kyosu/functions.hpp>

Callable Signatures

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

Parameters

• z : value to process.

Return value

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

Note

ζ can be used as an alias of zeta.

External references

• Wikipedia: Dirichlet series

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};
  auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
  std::cout << "---- simd" << std::endl
            << "<- zc          = " << zc << std::endl
            << "<- ref1        = " << ref1 << std::endl
            << "-> zeta(zc)    = " << kyosu::zeta(zc) << std::endl
            << "-> zeta(ref1)  = " << kyosu::zeta(ref1) << std::endl
            << "-> ζ(ref1)       " << kyosu::ζ(ref1) << std::endl;
  return 0;
}