DOI: 10.54287/gujsa.1955590 ISSN: 2147-9542

Finite Sums Involving Special Polynomials and Numbers via Inverse Difference Operators

Elif Şükrüoğlu, Yılmaz Şimşek
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Finite and infinite sums play a significant role in various fields of applied mathematics, discrete analysis, and operator theory. In this paper, we derive several identities involving the inverse difference operator and generalized array polynomials. By applying the inverse difference operator to generalized array polynomials, new representations are obtained involving Bernoulli polynomials and numbers, Stirling numbers, and some special numbers. Furthermore, various finite sum identities and combinatorial relations are established through generating functions and finite difference techniques. The results provide alternative representations for the inverse difference operator and can contribute to further studies in finite difference analysis, combinatorics, and special functions.

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