Logarithmic Integral Function - Asymptotic Expansion

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.