Some results on derangement polynomials

[摘要] 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 0. For the higher moments, we obtain a multiple integral representation of the order of the moment under computation.

[学科分类] 物理化学和理论化学

[关键词] derangement;permutation;integration