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.

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