论文标题
Baker-Campbell-Hausdorff系列系数的分母
Denominators of coefficients of the Baker-Campbell-Hausdorff series
论文作者
论文摘要
为了计算Baker-campbell-Hausdorff系列$ h = \ log（e^ae^b}）$的术语，某些先验知识对该系列系数的分母可能是有益的。在本文中，得出了该系列均匀组件的合理系数的共同分母的明确公式。直到30度的显式计算表明，该公式获得的共同分母尽可能小，这表明该公式在某种意义上是最佳的。从数字理论的角度来看，由公式定义的整数序列似乎也很有趣。例如，与Bernoulli数字和Bernoulli多项式的分母有联系。
For the computation of terms of the Baker-Campbell-Hausdorff series $H = \log(e^Ae^B})$ some a priori knowledge about the denominators of the coefficients of the series can be beneficial. In this paper an explicit formula for the computation of common denominators for the rational coefficients of the homogeneous components of the series is derived. Explicit computations up to degree 30 show that the common denominators obtained by this formula are as small as possible, which suggests that the formula is in a sense optimal. The sequence of integers defined by the formula seems to be interesting also from a number-theoretic point of view. There is, e.g., a connection with the denominators of the Bernoulli numbers and the Bernoulli polynomials.
