Asymptotic Expansion
The asymptotic behavior for x → ∞ is
where is the big O notation. The full asymptotic expansion is
or
Note that, as an asymptotic expansion, this series is not convergent: it is a reasonable approximation only if the series is truncated at a finite number of terms, and only large values of x are employed. This expansion follows directly from the asymptotic expansion for the exponential integral.
Read more about this topic: Logarithmic Integral Function
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