In this paper, the authors extend the theory of the generalized difference operator (…) .to the generalized difference operator of the n-th kind denoted by (…), where L =(…)of positive reals (…) and obtain some intresting 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 general partial sums of products of several powers of consecutive terms of an arithmetic progression in number theory are derived.
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