Some Identities on Truncated Polynomials Associated with Degenerate Bell Polynomials

The aim of this paper is to introduce truncated degenerate Bell polynomials and numbers and to investigate some of their properties. In more detail, we obtain explicit expressions, identities involving other special polynomials, integral representations, a Dobinski-like formula and expressions of th...

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Bibliographic Details
Published inRussian journal of mathematical physics Vol. 28; no. 3; pp. 342 - 355
Main Authors Kim, T., Kim, D. S.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.07.2021
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Combinatorial analysis
Differential equations
Gamma function
Mathematical and Computational Physics
Operators (mathematics)
Physics
Physics and Astronomy
Polynomials
Random variables
Theoretical
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Summary:The aim of this paper is to introduce truncated degenerate Bell polynomials and numbers and to investigate some of their properties. In more detail, we obtain explicit expressions, identities involving other special polynomials, integral representations, a Dobinski-like formula and expressions of the generating function in terms of differential operators and the linear incomplete gamma function. In addition, we introduce truncated degenerate modified Bell polynomials and numbers and obtain similar results for those polynomials. As an application of our results, we show that the truncated degenerate Bell numbers can be expressed as a finite sum involving moments of a beta random variable with certain parameters.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1061-9208
1555-6638
DOI:10.1134/S1061920821030079