exp_int

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