Some Identities of the Degenerate Higher Order Derangement Polynomials and Numbers
Recently, Kim-Kim (J. Math. Anal. Appl. (2021), Vol. 493(1), 124521) introduced the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-Sheffer...
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MDPI AG
2021-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/2/176 |
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| author | Hye Kyung Kim |
| author_facet | Hye Kyung Kim |
| author_sort | Hye Kyung Kim |
| collection | DOAJ |
| description | Recently, Kim-Kim (J. Math. Anal. Appl. (2021), Vol. 493(1), 124521) introduced the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-Sheffer sequence and the degenerate Sheffer sequence. In addition, Kim et al. (arXiv:2011.08535v1 17 November 2020) studied the degenerate derangement polynomials and numbers, and investigated some properties of those polynomials without using degenerate umbral calculus. In this paper, the y the degenerate derangement polynomials of order <i>s</i> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi></mrow></semantics></math></inline-formula>) and give a combinatorial meaning about higher order derangement numbers. In addition, the author gives some interesting identities related to the degenerate derangement polynomials of order <i>s</i> and special polynomials and numbers by using degenerate Sheffer sequences, and at the same time derive the inversion formulas of these identities. |
| first_indexed | 2024-03-09T03:57:18Z |
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| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T03:57:18Z |
| publishDate | 2021-01-01 |
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| series | Symmetry |
| spelling | doaj.art-34d1e7f2ab554cffa8ce1c106ee87bc52023-12-03T14:18:34ZengMDPI AGSymmetry2073-89942021-01-0113217610.3390/sym13020176Some Identities of the Degenerate Higher Order Derangement Polynomials and NumbersHye Kyung Kim0Department of Mathematics Education, Daegu Catholic University, Gyeongsan 38430, KoreaRecently, Kim-Kim (J. Math. Anal. Appl. (2021), Vol. 493(1), 124521) introduced the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-Sheffer sequence and the degenerate Sheffer sequence. In addition, Kim et al. (arXiv:2011.08535v1 17 November 2020) studied the degenerate derangement polynomials and numbers, and investigated some properties of those polynomials without using degenerate umbral calculus. In this paper, the y the degenerate derangement polynomials of order <i>s</i> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi></mrow></semantics></math></inline-formula>) and give a combinatorial meaning about higher order derangement numbers. In addition, the author gives some interesting identities related to the degenerate derangement polynomials of order <i>s</i> and special polynomials and numbers by using degenerate Sheffer sequences, and at the same time derive the inversion formulas of these identities.https://www.mdpi.com/2073-8994/13/2/176derangement numbers and polynomialsdegenerate derangement numbers and polynomialsLah–Bell numbers and polynomialsthe degenerate Sheffer sequencethe degenerate Bernoulli (Euler) polynomialsthe degenerate Frobenius–Euler polynomials |
| spellingShingle | Hye Kyung Kim Some Identities of the Degenerate Higher Order Derangement Polynomials and Numbers Symmetry derangement numbers and polynomials degenerate derangement numbers and polynomials Lah–Bell numbers and polynomials the degenerate Sheffer sequence the degenerate Bernoulli (Euler) polynomials the degenerate Frobenius–Euler polynomials |
| title | Some Identities of the Degenerate Higher Order Derangement Polynomials and Numbers |
| title_full | Some Identities of the Degenerate Higher Order Derangement Polynomials and Numbers |
| title_fullStr | Some Identities of the Degenerate Higher Order Derangement Polynomials and Numbers |
| title_full_unstemmed | Some Identities of the Degenerate Higher Order Derangement Polynomials and Numbers |
| title_short | Some Identities of the Degenerate Higher Order Derangement Polynomials and Numbers |
| title_sort | some identities of the degenerate higher order derangement polynomials and numbers |
| topic | derangement numbers and polynomials degenerate derangement numbers and polynomials Lah–Bell numbers and polynomials the degenerate Sheffer sequence the degenerate Bernoulli (Euler) polynomials the degenerate Frobenius–Euler polynomials |
| url | https://www.mdpi.com/2073-8994/13/2/176 |
| work_keys_str_mv | AT hyekyungkim someidentitiesofthedegeneratehigherorderderangementpolynomialsandnumbers |