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Some results on derangement polynomials

Mehdi Hassani, Hossein Moshtagh, Mohammad 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.

Sur la série de Lagrange

G. Zolotareff (1876)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

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