Finite Sums Involving Special Polynomials and Numbers via Inverse Difference Operators

Elif Şükrüoğlu; Yılmaz Şimşek

doi:10.54287/gujsa.1955590

Finite Sums Involving Special Polynomials and Numbers via Inverse Difference Operators

Abstract

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.

Keywords

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References

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Elif Şükrüoğlu ^*
0000-0003-3986-0246
Türkiye

Yılmaz Şimşek
0000-0002-0611-7141
Türkiye

Early Pub Date

September 23, 2026

Publication Date

-

Submission Date

May 20, 2026

Acceptance Date

July 20, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.54287/gujsa.1955590

IZ

https://izlik.org/JA39NM35ES

Cite

RIS / Bibtex

APA

Şükrüoğlu, E., & Şimşek, Y. (2026). Finite Sums Involving Special Polynomials and Numbers via Inverse Difference Operators. Gazi University Journal of Science Part A: Engineering and Innovation, Advanced Online Publication, 1065-1080. https://doi.org/10.54287/gujsa.1955590

AMA

1.Şükrüoğlu E, Şimşek Y. Finite Sums Involving Special Polynomials and Numbers via Inverse Difference Operators. GU J Sci, Part A. 2026;(Advanced Online Publication):1065-1080. doi:10.54287/gujsa.1955590

Chicago

Şükrüoğlu, Elif, and Yılmaz Şimşek. 2026. “Finite Sums Involving Special Polynomials and Numbers via Inverse Difference Operators”. Gazi University Journal of Science Part A: Engineering and Innovation, no. Advanced Online Publication: 1065-80. https://doi.org/10.54287/gujsa.1955590.

EndNote

Şükrüoğlu E, Şimşek Y (September 1, 2026) Finite Sums Involving Special Polynomials and Numbers via Inverse Difference Operators. Gazi University Journal of Science Part A: Engineering and Innovation Advanced Online Publication 1065–1080.

IEEE

[1]E. Şükrüoğlu and Y. Şimşek, “Finite Sums Involving Special Polynomials and Numbers via Inverse Difference Operators”, GU J Sci, Part A, no. Advanced Online Publication, pp. 1065–1080, Sept. 2026, doi: 10.54287/gujsa.1955590.

ISNAD

Şükrüoğlu, Elif - Şimşek, Yılmaz. “Finite Sums Involving Special Polynomials and Numbers via Inverse Difference Operators”. Gazi University Journal of Science Part A: Engineering and Innovation. Advanced Online Publication (September 1, 2026): 1065-1080. https://doi.org/10.54287/gujsa.1955590.

JAMA

1.Şükrüoğlu E, Şimşek Y. Finite Sums Involving Special Polynomials and Numbers via Inverse Difference Operators. GU J Sci, Part A. 2026;:1065–1080.

MLA

Şükrüoğlu, Elif, and Yılmaz Şimşek. “Finite Sums Involving Special Polynomials and Numbers via Inverse Difference Operators”. Gazi University Journal of Science Part A: Engineering and Innovation, no. Advanced Online Publication, Sept. 2026, pp. 1065-80, doi:10.54287/gujsa.1955590.

Vancouver

1.Elif Şükrüoğlu, Yılmaz Şimşek. Finite Sums Involving Special Polynomials and Numbers via Inverse Difference Operators. GU J Sci, Part A. 2026 Sep. 1;(Advanced Online Publication):1065-80. doi:10.54287/gujsa.1955590