  According to generalized Mellin derivative (Kargin), we introduce a new
family of polynomials called higher order generalized geometric polynomials. We
obtain some properties of them.We discuss their connections to degenerate
Bernoulli and Euler polynomials. Furthermore, we find new formulas for the
Carlitz's (Carlitz) and Howard's (Howard2) finite sums. Finally, we evaluate
several series in closed forms, one of which has the coefficients include
values of the Riemann zeta function. Moreover, we calculate some integrals in
terms of generalized geometric polynomials.
