The Generalized Difference Operator of the n^th Kind

In this chapter, the authors extend the theory of the generalized difference Operator ∆L to the generalized difference operator of the n^thkind denoted by ∆L Where L =L={l_1,l_2,….l_n} of positive realsl_1,l_2,….l_nand obtain some interesting results on the relation between the generalized polynomial factorial of the first kind, n^thkind 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.