Some results on derangement polynomials

Mehdi Hassani; Hossein Moshtagh; Mohammad Ghorbani

Commentationes Mathematicae Universitatis Carolinae (2022)

  • Volume: 62 63, Issue: 3, page 307-313
  • ISSN: 0010-2628

Abstract

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We study moments of the difference D n ( x ) - x n n ! 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.

How to cite

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Hassani, Mehdi, Moshtagh, Hossein, and Ghorbani, Mohammad. "Some results on derangement polynomials." Commentationes Mathematicae Universitatis Carolinae 62 63.3 (2022): 307-313. <http://eudml.org/doc/299037>.

@article{Hassani2022,
abstract = {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.},
author = {Hassani, Mehdi, Moshtagh, Hossein, Ghorbani, Mohammad},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {derangement; permutation; integration},
language = {eng},
number = {3},
pages = {307-313},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some results on derangement polynomials},
url = {http://eudml.org/doc/299037},
volume = {62 63},
year = {2022},
}

TY - JOUR
AU - Hassani, Mehdi
AU - Moshtagh, Hossein
AU - Ghorbani, Mohammad
TI - Some results on derangement polynomials
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2022
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62 63
IS - 3
SP - 307
EP - 313
AB - 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.
LA - eng
KW - derangement; permutation; integration
UR - http://eudml.org/doc/299037
ER -

References

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