The Generalized Difference Operator of the n^th Kind

In this chapter, the authors extend the theory of the generalized difference Operator δL to the generalized difference operator of the n^th kind denoted by δL Where L = L = {l₁, l₂,…., l_n} of positive reals l₁, l₂,…., l_n and obtain some interesting results on the relation between the generalized polynomial factorial of the first kind, n^th kind and algebraic polynomials. Also formulae for the sum of the general partial sums of products of several powers of consecutive terms of an Arithmetic progression in number theory are derived.