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Title: Some results on derangement polynomials (English)
Author: Hassani, Mehdi
Author: Moshtagh, Hossein
Author: Ghorbani, Mohammad
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 63
Issue: 3
Year: 2022
Pages: 307-313
Summary lang: English
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Category: math
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Summary: We study moments of the difference $D_n(x)-x^n n! {\rm e}^{-1/x}$ concerning derangement polynomials $D_n(x)$. For the first moment, we obtain an explicit formula in terms of the exponential integral function and we show that it is always negative for $x>0$. For the higher moments, we obtain a multiple integral representation of the order of the moment under computation. (English)
Keyword: derangement
Keyword: permutation
Keyword: integration
MSC: 05A05
MSC: 05A16
MSC: 26A06
idZBL: Zbl 07655802
idMR: MR4542791
DOI: 10.14712/1213-7243.2022.025
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Date available: 2023-02-01T12:04:38Z
Last updated: 2024-10-04
Stable URL: http://hdl.handle.net/10338.dmlcz/151478
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