tricomi

kyosu::tricomi = eve::functor<tricomi_t>

inlineconstexpr

Computes the tricomi function \(U\) also called confluent hypergeometric function of the second kind.

Defined in Header

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
  constexpr auto tricomi(auto z, auto a, auto b) noexcept;
}

Parameters

• a, b, z: real or complex inputs.

Return value

Returns the value at z of the confluent hypergeometric function of the second kind

External references

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

  Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
  auto I = kyosu::complex(0.0, 1.0);
  std::cout << "tricomi(2.0, 1, 1.5)         "<< kyosu::tricomi(2.0, 1, 1.5)        << std::endl;
  std::cout << "tricomi(2.0, 1, I)           "<< kyosu::tricomi(2.0, 1, I)          << std::endl;
  std::cout << "tricomi( 1.72725307941437, 0.0, 0.0)  "<< kyosu::tricomi( 1.72725307941437, 0.0, 0.0) << std::endl;
  std::cout << "tricomi( 1.72725307941437, 1.0, 1.0)  "<< kyosu::tricomi( 1.72725307941437, 1.0, 1.0) << std::endl;
  std::cout << "tricomi( 1.72725307941437, 2.0, 2.0)  "<< kyosu::tricomi( 1.72725307941437, 2.0, 2.0) << std::endl;
  std::cout << "tricomi( 1.72725307941437, 3.0, 3.0)  "<< kyosu::tricomi( 1.72725307941437, 3.0, 3.0) << std::endl;
  std::cout << "tricomi( 1.72725307941437+I, 0.0, 0.0)  "<< kyosu::tricomi( 1.72725307941437+I, 0.0, 0.0) << std::endl;
  std::cout << "tricomi( 1.72725307941437+I, 1.0, 1.0)  "<< kyosu::tricomi( 1.72725307941437+I, 1.0, 1.0) << std::endl;
  std::cout << "tricomi( 1.72725307941437+I, 2.0, 2.0)  "<< kyosu::tricomi( 1.72725307941437+I, 2.0, 2.0) << std::endl;
  std::cout << "tricomi( 1.72725307941437+I, 3.0, 3.0)  "<< kyosu::tricomi( 1.72725307941437+I, 3.0, 3.0) << std::endl;
  return 0;
}