Polynomial formulations of Multivariable Arithmetic Progressions of Alternating Powers

Taking inspiration from the work of Lanphier \cite{LANPHIER2022125716}, a generalized multivariable polynomial formulation for sums of alternating powers is given, as well as analogous sums. Furthermore, an analog of the Euler-Maclaurin Summation Formula is established and used to give asymptotic formulas for multivariable-type Lerch-Hurwitz zeta functions.