kummer

auto kyosu::kummer = eve::functor<kummer_t>

inlineconstexpr

Computes the Kummer function (confluent hypergeometric function of the first kind) \(M\) (which is an other name for the hypergeometric function \({}_1F_1\)) and it regularized version \(\mathbf{M}\).

Defined in Header

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   //regular call
  constexpr auto kummer(auto z, auto a, auto b) noexcept;             //1
 
   // Semantic modifyiers
  constexpr auto kummer[regularized](auto z, auto a, auto b) noexcept;//2
 
 
}

Parameters

• a, b, z: real or complex inputs.

Return value

1. Returns the value at z of the Kummer function with a and b parameters. The call kummer(z, a, b) is equivalent to hypergeometric(z, kumi::tuple{a}, kumi::tuple{b})
2. With the regularized options, returns the value at z of the Regularized Kummer function \(\mathbf{M}\), i.e. \(M\) divided by \(\Gamma(b)\), well defined even if b is a negative integer.

External references

• DLMF: Kummer Functions
• Wolfram MathWorld:Confluent Hypergeometric Function of the Second Kind
• Wikipedia: Confluent hypergeometric function

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
  auto I = kyosu::complex(0.0, 1.0);
  std::cout << "kummer(2.0, 1., 1.5)                 " << kyosu::kummer(2.0, 1., 1.5) << std::endl;
  std::cout << "kummer(2.0, 1., I)                   " << kyosu::kummer(2.0, 1., I) << std::endl;
  std::cout << "kummer[regularized](2.0, 1., 1.5)    " << kyosu::kummer[kyosu::regularized](2.0, 1., 1.5) << std::endl;
  std::cout << "kummer[regularized](2.0, 1., I)      " << kyosu::kummer[kyosu::regularized](2.0, 1., I) << std::endl;
  std::cout << "kummer[regularized](0.5, -2.0,-1.0)  " << kyosu::kummer[kyosu::regularized](1.0, 2.0, -3.0)
            << std::endl;
  std::cout << "kummer[regularized](0.5, -2.0,-1.0)  " << kyosu::kummer[kyosu::regularized](1.0, 2.0, -3.001)
            << std::endl;
  return 0;
}