In this paper, the author define the
generalized q-derivative oprator and obtain its relation
with shift operator.Also, we present the discrete version
of Leibtz theorem according to the generalized qderivative operator.By defining its inverse,and using
Stirling numbers of first kind, we establish formula for
the sum of higher power of geometric progression in the
field of first of Number Analysis.
Keywords :
Generalized q-Derivative Operator, Polynomial Factorial, Geometric Progression