exp_int

auto kyosu::exp_int = eve::functor<exp_int_t>

inlineconstexpr

elementwise_callable object computing the exponential integral \( \mathbf{E}_n(x) = \displaystyle \int_1^\infty \frac{e^{-xt}}{t^n}\;\mbox{d}t\).

Header file

#include <eve/module/special.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto exp_int(concepts::cayley_dickson auto x)                                   noexcept; // 1
   constexpr auto exp_int(concepts::cayley_dickson auto n, floating_value auto x)            noexcept; // 2
}

Parameters

• n: order. cayley_dickson or real argument. If not present taken to be 1.
• x: cayley_dickson or real argument.

Return value

1. The value of the exponential integral \( \mathbf{E}_n(x) = \displaystyle \int_1^\infty \frac{e^{-xt}}{t^n}\;\mbox{d}t\), is returned.
2. The operation is performed conditionnaly.

External references

• Wolfram MathWorld:Exponential Integral
• DLMF: Generalized Exponential Integral
• Wikipedia: Exponential integral

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
  using kyosu::complex_t;
  using kyosu::exp;
  using kyosu::quaternion_t;
  using e_t = float;
  using c_t = kyosu::complex_t<float>;
  using q_t = kyosu::quaternion_t<float>;
  using we_t = eve::wide<e_t, eve::fixed<2>>;
  using wc_t = eve::wide<c_t, eve::fixed<2>>;
  using wq_t = eve::wide<q_t, eve::fixed<2>>;
 
  using kyosu::exp_int;
  std::cout << "Real:        \n";
  e_t e(2.9f);
  we_t we = we_t(e);
  std::cout << e << " -> " << exp_int(e) << "\n";
  std::cout << we << " -> " << exp_int(we) << "\n";
  std::cout << exp_int(c_t(e)) << "\n";
  std::cout << exp_int(q_t(e)) << "\n";
  std::cout << exp_int(wc_t(e)) << "\n";
  std::cout << exp_int(wq_t(e)) << "\n";
 
  std::cout << "Complex:     \n";
  c_t c(3.5f, -2.9f);
  wc_t wc = wc_t(c);
  std::cout << c << " -> " << exp_int(c) << "\n";
  std::cout << wc << " -> " << exp_int(wc) << "\n";
  std::cout << exp_int(q_t(c)) << "\n";
  std::cout << exp_int(wq_t(c)) << "\n";
 
  std::cout << "Quaternion:  \n";
  q_t q(3.5f, -2.9f, 2.1f, 3.2f);
  wq_t wq = wq_t(q);
  std::cout << q << " -> " << exp_int(q) << "\n";
  std::cout << wq << " -> " << exp_int(wq) << "\n";
 
  return 0;
}