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Some results on derangement polynomials

Mehdi HassaniHossein MoshtaghMohammad Ghorbani — 2022

Commentationes Mathematicae Universitatis Carolinae

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.

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