Degenerate Derangement Polynomials and Numbers
| Autor: | Dongkyu Lim, Minyoung Ma |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Pure mathematics Polynomial fully degenerate Bell polynomials degenerate derangement polynomials Type (model theory) 01 natural sciences Computer Science::Digital Libraries Bell polynomials degenerate Stirling numbers Fubini's theorem degenerate derangement polynomials of the second kind degenerate gamma distribution QA1-939 Stirling number 0101 mathematics Mathematics QA299.6-433 Recurrence relation Mathematics::Combinatorics 010102 general mathematics Degenerate energy levels degenerate Fubini polynomials Statistical and Nonlinear Physics 010101 applied mathematics Derangement Thermodynamics QC310.15-319 Analysis |
| Zdroj: | Fractal and Fractional, Vol 5, Iss 59, p 59 (2021) Fractal and Fractional Volume 5 Issue 3 |
| ISSN: | 2504-3110 |
| Popis: | In this paper, we consider a new type of degenerate derangement polynomial and number, which shall be called the degenerate derangement polynomials and numbers of the second kind. These concepts are motivated by Kim et al.’s work on degenerate derangement polynomials and numbers. We investigate some properties of these new degenerate derangement polynomials and numbers and explore their connections with the degenerate gamma distributions for the case λ∈(−1,0). In more detail, we derive their explicit expressions, recurrence relations, and some identities involving our degenerate derangement polynomials and numbers and other special polynomials and numbers, which include the fully degenerate Bell polynomials, the degenerate Fubini polynomials, and the degenerate Stirling numbers of the first and the second kinds. We also show that those polynomials and numbers are connected with the moments of some variants of the degenerate gamma distributions. Moreover, we compare the degenerate derangement polynomials and numbers of the second kind to those of Kim et al. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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