  We extend the Faulhaber formula to the whole complex plane, obtaining an
expression that fully resembles the Euler-Maclaurin summation formula, only
it's exact. Thereafter, an expression for the generalized harmonic progressions
valid in the whole complex plane is also derived. Lastly, we extend a formula
for the Hurwitz zeta function valid at the negative integers, $\zeta(-k,b)$, to
the whole complex plane, following a similar procedure.
