  We define a generalized class of modified zeta series transformations
generating the partial sums of the Hurwitz zeta function and series expansions
of the Lerch transcendent function. The new transformation coefficients we
define within the article satisfy expansions by generalized harmonic number
sequences, or the partial sums of the Hurwitz zeta function, which are
analogous to known properties for the Stirling numbers of the first kind and
for the known transformation coefficients employed to enumerate variants of the
polylogarithm function series. Applications of the new results we prove in the
article include new series expansions of the Dirichlet beta function, the
Legendre chi function, BBP-type series identities for special constants,
alternating and exotic Euler sum variants, alternating zeta functions with
powers of quadratic denominators, and particular series defining special cases
of the Riemann zeta function constants at the positive integers $s \geq 3$.
