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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 54 Issue: 4

Some properties of Appell type degenerate Bell polynomials

Zeynep Özat(GAZI UNIVERSITY)0000-0001-7896-5951
Mehmet Ali Özarslan(EASTERN MEDITARRANEAN UNIVERSITY)0000-0002-6473-9299
Bayram Çekim(GAZI UNIVERSITY)0000-0002-5363-2453
Pages
—
Publication Date
2025-08-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we establish theorems that provide various families of multilinear and multilateral generating functions for the Appell type degenerate Bell polynomials.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In recent years, the degenerate versions of some polynomial families such as Bernoulli, Euler, Apostol and Bell polynomials have been intensively studied in the literature.
📊
Key Findings & Data:Many new forms of Bell polynomials such as degenerate, partially degenerate and fully degenerate have attracted attention.
💡
Conclusion & Impact:Finally, we establish theorems that provide various families of multilinear and multilateral generating functions for the Appell type degenerate Bell polynomials.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Appell polynomials · Bell polynomials · degenerate Bell polynomials

Abstract

In recent years, the degenerate versions of some polynomial families such as Bernoulli, Euler, Apostol and Bell polynomials have been intensively studied in the literature. Many new forms of Bell polynomials such as degenerate, partially degenerate and fully degenerate have attracted attention. The specific aim of this paper is to introduce a new family of general degenerate Bell type polynomials with the help of degenerate Appell polynomials and explore their properties, including explicit form, determinant representation, recurrence relation, lowering and raising operators and difference equation. Then, after discussing the special cases of Appell type degenerate Bell polynomial families, new polynomial families including Bernoulli and Euler polynomials are given. Furthermore, corresponding results are obtained for these new families. Lastly, new relations and summation formulas are obtained including Stirling numbers and Appell type degenerate Bell polynomials. Finally, we establish theorems that provide various families of multilinear and multilateral generating functions for the Appell type degenerate Bell polynomials.

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Cite This Article

Özat, Z., Özarslan, M. A., Çekim, B. (2025). Some properties of Appell type degenerate Bell polynomials. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 4. https://doi.org/10.15672/hujms.1517317

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