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.

Read more about this topic:  Logarithmic Integral Function

Famous quotes containing the word expansion:

    The fundamental steps of expansion that will open a person, over time, to the full flowering of his or her individuality are the same for both genders. But men and women are rarely in the same place struggling with the same questions at the same age.
    Gail Sheehy (20th century)