  A difference equation analogue of the Knizhnik-Zamolodchikov equation is
exhibited by developing a theory of the generating function $H(z)$ of Hurwitz
polyzeta functions to parallel that of the polylogarithms. By emulating the
role of the KZ equation as a connection on a suitable bundle, a difference
equation version of the notion of connection is developed for which $H(z)$ is a
flat section. Solving a family of difference equations satisfied by the Hurwitz
polyzetas leads to the normalized multiple Bernoulli polynomials (NMBPs) as the
counterpart to the Hurwitz polyzeta functions, at tuples of negative integers.
A generating function for these polynomials satisfies a similar difference
equation to that of $H(z)$, but in contrast to the fact that said polynomials
have rational coefficients, the algebraic independence of the Hurwitz polyzeta
functions is proven. The values of the NMBPs at $z=1$ provide a regularization
of the multiple zeta values at tuples of negative integers, which is shown to
agree with the regularization given in work of S. Akiyama and collaborators.
Various elementary properties of these values are proven.
