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
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
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.
 [1]
Dragomir
Ž. Djoković, An elementary proof of the
BakerCampbellHausdorffDynkin formula, Math. Z. 143
(1975), no. 3, 209–211. MR 0399196
(53 #3047)
 [2]
M.
Eichler, A new proof of the BakerCampbellHausdorff formula,
J. Math. Soc. Japan 20 (1968), 23–25. MR 0223417
(36 #6465)
 [3]
R.
Gilmore, BakerCampbellHausdorff formulas, J. Mathematical
Phys. 15 (1974), 2090–2092. MR 0354944
(50 #7421)
 [4]
Karl
Goldberg, The formal power series for
𝑙𝑜𝑔𝑒^{𝑥}𝑒^{𝑦},
Duke Math. J. 23 (1956), 13–21. MR 0082571
(18,572f)
 [5]
Marshall
Hall Jr., A basis for free Lie rings and higher
commutators in free groups, Proc. Amer. Math.
Soc. 1 (1950),
575–581. MR 0038336
(12,388a), http://dx.doi.org/10.1090/S00029939195000383367
 [6]
Nathan
Jacobson, Lie algebras, Interscience Tracts in Pure and
Applied Mathematics, No. 10, Interscience Publishers (a division of John
Wiley & Sons), New YorkLondon, 1962. MR 0143793
(26 #1345)
 [7]
B.
V. Lidskiĭ, A polyhedron of the spectrum of the sum of two
Hermitian matrices, Funktsional. Anal. i Prilozhen.
16 (1982), no. 2, 76–77 (Russian). MR 659172
(83k:15009)
 [8]
Wilhelm
Magnus, On the exponential solution of differential equations for a
linear operator, Comm. Pure Appl. Math. 7 (1954),
649–673. MR 0067873
(16,790a)
 [9]
Wilhelm
Magnus, A connection between the BakerHausdorff formula and a
problem of Burnside, Ann. of Math. (2) 52 (1950),
111–126. MR 0038964
(12,476c)
 [10]
R.
D. Richtmyer and Samuel
Greenspan, Expansion of the CampbellBakerHausdorff formula by
computer, Comm. Pure Appl. Math. 18 (1965),
107–108. MR 0175292
(30 #5477)
 [11]
Olga
Taussky and John
Todd, Some discrete variable computations, Proc. Sympos. Appl.
Math., Vol. 10, American Mathematical Society, Providence, R.I., 1960,
pp. 201–209. MR 0115261
(22 #6063)
 [12]
R. C. Thompson, Lecture at the 1980 Auburn (Alabama) matrix conference organized by Emilie Haynsworth; three unpublished manuscripts.
 [13]
Robert
C. Thompson, Cyclic relations and the Goldberg
coefficients in the CampbellBakerHausdorff formula, Proc. Amer. Math. Soc. 86 (1982), no. 1, 12–14. MR 663855
(84e:17017), http://dx.doi.org/10.1090/S00029939198206638550
 [14]
Robert
C. Thompson, Author vs. referee: a case history for middle level
mathematicians, Amer. Math. Monthly 90 (1983),
no. 10, 661–668. MR 723938
(85c:01072), http://dx.doi.org/10.2307/2323528
 [15]
Robert
C. Thompson, Proof of a conjectured exponential formula,
Linear and Multilinear Algebra 19 (1986), no. 2,
187–197. MR
846553 (88b:15020), http://dx.doi.org/10.1080/03081088608817715
 [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 Inc., Englewood Cliffs, N.J., 1974.
PrenticeHall Series in Modern Analysis. MR 0376938
(51 #13113)
 [1]
 D. Ž. Djoković, "An elementary proof of the BakerCampbellHausdorffDynkin formula," Math. Z., v. 143, 1975, pp. 209211. MR 0399196 (53:3047)
 [2]
 M. Eichler, "A new proof of the BakerCampbellHausdorff formula," J. Math. Soc. Japan, v. 29, 1968, pp. 2335. MR 0223417 (36:6465)
 [3]
 R. Gilmore, "BakerCampbellHausdorff formulas," J. Math. Phys., v. 15, 1974, pp. 20902092. MR 0354944 (50:7421)
 [4]
 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)
 [7]
 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)
 [10]
 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)
 [12]
 R. C. Thompson, Lecture at the 1980 Auburn (Alabama) matrix conference organized by Emilie Haynsworth; three unpublished manuscripts.
 [13]
 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)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
17B05,
11Y99,
1704
Retrieve articles in all journals
with MSC:
17B05,
11Y99,
1704
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198708661149
PII:
S 00255718(1987)08661149
Article copyright:
© Copyright 1987 American Mathematical Society
