Some properties of Appell type degenerate Bell polynomials

Year 2025, Early Access, 1 - 24

Zeynep Özat , Mehmet Ali Özarslan , Bayram Çekim

https://doi.org/10.15672/hujms.1517317

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.

Keywords

Appell polynomials, Bell polynomials, degenerate Bell polynomials, Bell based Appell polynomials, Stirling numbers

References

• [1] A. Altın, E. Erkuş and M.A. Özarslan, Families of linear generating functions for polynomials in two variables, Integral Transforms and Special Functions, 17 (5), 315- 320, 2006.