  The method analytic continuation of operators acting integer n-times to
complex s-times (hep-th/9707206) is applied to an operator that generates
Bernoulli numbers B_n (Math. Mag. 70(1), 51 (1997)). B_n and Bernoulli
polynomials B_n(s) are analytic continued to B(s) and B_s(z). A new formula for
the Riemann zeta function zeta(s) in terms of nested series of zeta(n) is
derived. The new concept of dynamics of the zeros of analytic continued
polynomials is introduced, and an interesting phenonmenon of `scatterings' of
the zeros of B_s(z) is observed.
