Numerical values of Goldberg's coefficients in the series for
Authors:
Morris Newman and Robert C. Thompson
Journal:
Math. Comp. 48 (1987), 265271
MSC:
Primary 17B05; Secondary 11Y99, 1704
MathSciNet review:
866114
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Abstract 
References 
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Additional Information
Abstract: The coefficients of K. Goldberg in the infinite series for for noncommuting x and y are computed as far as words of length twenty.
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 K. Goldberg, "The formal power series for ," Duke Math. J., v. 23, 1956, pp. 1321. MR 0082571 (18:572f)
 [5]
 M. Hall, Jr., "A basis for free Lie rings and higher commutators in free groups," Proc. Amer. Math. Soc., v. 1, 1950, pp. 575581. MR 0038336 (12:388a)
 [6]
 N. Jacobson, Lie Algebras, Wiley, New York, 1962. MR 0143793 (26:1345)
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 B. V. Lidskiĭ, "Spectral polyhedron of a sum of two hermitian matrices," Functional Anal. Appl., v. 16, 1982, pp. 139140. MR 659172 (83k:15009)
 [8]
 W. Magnus, "On the exponential solution of differential equations for a linear operator," Comm. Pure Appl. Math., v. 7, 1954, pp. 649673. MR 0067873 (16:790a)
 [9]
 W. Magnus, "A connection between the BakerHausdorff formula and a problem of Burnside," Ann. of Math., v. 52, 1950, pp. 111126, and v. 57, 1953, p. 606. MR 0038964 (12:476c)
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 R. D. Richtmyer & Samuel Greenspan, "Expansion of the CampbellBakerHausdorff formula by computer," Comm. Pure Appl. Math., v. 18, 1965, pp. 107108. MR 0175292 (30:5477)
 [11]
 Olga Taussky & John Todd, Some Discrete Variable Computations, Proc. Sympos. Appl. Math., vol. 10, Amer. Math. Soc., Providence, R. I., 1958, pp. 201209. MR 0115261 (22:6063)
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 R. C. Thompson, Lecture at the 1980 Auburn (Alabama) matrix conference organized by Emilie Haynsworth; three unpublished manuscripts.
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 R. C. Thompson, "Cyclic relations and the Goldberg coefficients in the CampbellBakerHausdorff formula," Proc. Amer. Math. Soc., v. 86, 1982, pp. 1214. MR 663855 (84e:17017)
 [14]
 R. C. Thompson, "Author vs. referee: a case history for middle level mathematicians," Amer. Math. Monthly, v. 90, 1983, pp. 661668. MR 723938 (85c:01072)
 [15]
 R. C. Thompson, "Proof of a conjectured exponential formula," Linear and Multilinear Algebra, v. 19, 1986, pp. 187197. MR 846553 (88b:15020)
 [16]
 J. Todd, "Comment on previous selfstudy answer," Ann. Hist. Comput., v. 7, 1985, p. 69.
 [17]
 V. S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations, PrenticeHall, Englewood Cliffs, N. J., 1974. MR 0376938 (51:13113)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198708661149
PII:
S 00255718(1987)08661149
Article copyright:
© Copyright 1987
American Mathematical Society
