  Here, we study both analytically and numerically, an integral $Z(\sigma,r)$
related to the mean value of a generalized moment of Riemann's zeta function.
Analytically, we predict finite, but discontinuous values and verify the
prediction numerically, employing a modified form of Ces\`aro summation.
Further, it is proven and verified numerically that for certain values of
$\sigma$, the derivative function $Z^{\prime}(\sigma,n)$ equates to one
generalized tine of the Dirac comb function without recourse to the use of
limits, test functions or distributions. A surprising outcome of the numerical
study arises from the observation that the proper integral form of the
derivative function is quasi-periodic, which in turn suggests a periodicity of
the integrand. This possibility is also explored and it is found experimentally
that zeta function values offset (shifted) over certain segments of the
imaginary complex number line are moderately auto-correlated.
