hurwitz

auto eve::hurwitz = functor<hurwitz_t>

inlineconstexpr

Header file

#include <eve/module/special.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto hurwitz(floating_value auto x)                          noexcept; // 1
 
   // Lanes masking
   constexpr auto hurwitz[conditional_expr auto c](floating_value auto x) noexcept; // 2
   constexpr auto hurwitz[logical_value auto m](floating_value auto x)    noexcept; // 2
}

Parameters

• x: floating_value.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. The value of the Hurwitz function: \(\sum_{k=0}^\infty (k+z)^{-s}\), where any term with \(k+z = 0\) is excluded.
2. The operation is performed conditionnaly.

External references

• DLMF: Gamma and Psi Functions
• Wolfram MathWorld: Hurwitz Function

Example

// revision 1
#include <eve/module/special.hpp>
#include <iostream>
 
int main()
{
  eve::wide<double, eve::fixed<4>> z{0.125, 15, -2.45, 1.0};
 
  for(int i=2; i < 5 ; ++i)
  {
    std::cout << eve::hurwitz(i, z) << std::endl;
  }
//   using w_t =  eve::wide<double, eve::fixed<1>>;
//   std::cout << eve::hurwitz(3.0, 15.0) << std::endl;
//   std::cout << " ================================ "<< std::endl;
//   std::cout << eve::hurwitz(3.0, w_t(15.0)) << std::endl;
}