Series involving rational, factorial and power functions

Abstract: This is an anthology of series involving rational, factorial, and power functions expressed in terms of special functions. New finite expansions involving quotient functions expressed in terms of the Hurwitz-Lerch zeta function are given. These results represent a new form of expressing this special function as a finite series where contour integration is required for derivation. Extended series previously known and derived are extended using differential equations and algebraic methods.