  We develop series representations for the Hurwitz and Riemann zeta functions
in terms of generalized Bernoulli numbers (N\"{o}rlund polynomials), that give
the analytic continuation of these functions to the entire complex plane.
Special cases yield series representations of a wide variety of special
functions and numbers, including log Gamma, the digamma, and polygamma
functions. A further byproduct is that $\zeta(n)$ values emerge as nonlinear
Euler sums in terms of generalized harmonic numbers. We additionally obtain
series and integral representations of the first Stieltjes constant
$\gamma_1(a)$. The presentation unifies some earlier results.
