Polygamma Function - Asymptotic Expansion

Asymptotic Expansion

These non-converging series can be used to get quickly an approximation value with a certain numeric at-least-precision for large arguments:

and

\psi^{(0)}(z) = \ln(z) - \sum_{k=1}^\infty \frac{B_k}{k z^k}

where we have chosen, i.e. the Bernoulli numbers of the second kind.

Read more about this topic:  Polygamma 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)