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Theory and application of the generalized difference operator of the n-th kind (part I)

Susai Manuel M. M., Xavier G. B. A., Chandrasekar V., Pugalarasu R.

Demonstratio Mathematica

2012

Vol. 45, nr 1

94-106

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.