该级数
 |
(1)
|
对于非交换变量 
和 
。前几项是
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
该级数也可以推广到
 |
(6)
|
(Reinsch 2000)，给出前几项为
 |  |  |
(7)
|
 |  |  |
(8)
|
Baker-Campbell-Hausdorff 级数
使用 Wolfram|Alpha 探索
参考文献
Bose, A. "Dynkin's Method of Computing the Terms of the Baker-Campbell-Hausdorff Series." J. Math. Phys. 30, 2035-2037, 1989.Dynkin, E. B. "On the Representation by Means of Commutators of the Series
for Noncommuting 
." Mat. Sb. 25, 155-162, 1949.Gilmore, R. "Baker-Campbell-Hausdorff Formulas." J. Math. Phys. 15, 2090-2092, 1974.Goldberg, K. "The Formal Power Series for 
." Duke Math. J. 23, 13-21, 1956.Kobayashi, H.; Hatano, N.; and Suzuki, M. "Goldberg's Theorem and the Baker-Campbell-Hausdorff Formula." Physica A 250, 535-548, 1998.Magnus, W. A. Ann. Math. 52, 111, 1952.Magnus, W. A. Comm. Pure Appl. Math. 7, 649, 1954.Munthe-Kaas, H. and Owren, B. "Computations in a Free Lie Algebra." Philos. Trans. Roy. Soc. London A 357, 957-981, 1999.Newman, M. and Thompson, R. C. "Numerical Values of Goldberg's Coefficients in the Series for 
." Math. Comput. 48, 265-271, 1987.Oteo, J. A. "The Baker-Campbell-Hausdorff Formula and Nested Commutator Identities." J. Math. Phys. 32, 419-424, 1991.Reinsch, M. W. "A Simple Expression for the Terms in the Baker-Campbell-Hausdorff Series." 13 Jan 2000. http://arxiv.org/abs/math-ph/9905012.Reutenauer, C. "Algebraic Properties." Ch. 3 in Free Lie Algebras. New York: Oxford University Press, 1993.Thompson, R. C. "Cyclic Relations and the Goldberg Coefficients in the Campbell-Baker-Hausdorff Formula." Proc. Amer. Math. Soc. 86, 12-14, 1982.Weiss, G. H. and Maradudin, A. A. "The Baker-Hausdorff Formula and a Problem in Crystal Physics." J. Math. Phys. 3, 771-777, 1962.在 Wolfram|Alpha 中被引用
Baker-Campbell-Hausdorff 级数请引用为
Weisstein, Eric W. "Baker-Campbell-Hausdorff 级数。" 来自 MathWorld--Wolfram Web 资源。 https://mathworld.net.cn/Baker-Campbell-HausdorffSeries.html