Hurwitz Zeta Function - Special Cases and Generalizations

Special Cases and Generalizations

The Hurwitz zeta function with non-negative integer m is related to the polygamma function:

For negative integer −n the values are related to the Bernoulli polynomials:

The Barnes zeta function generalizes the Hurwitz zeta function.

The Lerch transcendent generalizes the Hurwitz zeta:

$\Phi(z, s, q) = \sum_{k=0}^\infty \frac { z^k} {(k+q)^s}$

and thus

Hypergeometric function

where

Meijer G-function

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