polygamma

eve::polygamma = functor<polygamma_t>

inlineconstexpr

Header file

#include <eve/module/special.hpp>

Callable Signatures

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

Parameters

• n: scalar_value. (see note below)
• x: flaoting value.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. The value of the Polygamma function: \(\psi(n, x) = \frac{\mbox{d}^{n+1}}{\mbox{d}x^{n+1}}\log\Gamma(x)\) is returned.
2. The operation is performed conditionnaly.

Note

Only integral (or flint) positive values of n correspond to the proper polygamma definition. You can use non integral values but the function result may be different to the standard definitions of polygamma extensions.

External references

• DLMF: Gamma and Psi Functions
• Wolfram MathWorld: Polygamma 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=0; i < 5 ; ++i)
  {
    std::cout << eve::polygamma(i, z) << std::endl;
  }
}