# Asymptotic Expansion for Exponential Integral Function

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## Theorem

$\ds \map \Ei x \sim \frac {e^{-x} } x \sum_{n \mathop = 0}^\infty \paren {-1}^n \frac {n!} {x^n}$

where:

$\Ei$ is the exponential integral function
$\sim$ denotes asymptotic equivalence as $x \to \infty$.