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A038517
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Decimal expansion of Gauss-Kuzmin-Wirsing constant.
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5
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3, 0, 3, 6, 6, 3, 0, 0, 2, 8, 9, 8, 7, 3, 2, 6, 5, 8, 5, 9, 7, 4, 4, 8, 1, 2, 1, 9, 0, 1, 5, 5, 6, 2, 3, 3, 1, 1, 0, 8, 7, 7, 3, 5, 2, 2, 5, 3, 6, 5, 7, 8, 9, 5, 1, 8, 8, 2, 4, 5, 4, 8, 1, 4, 6, 7, 2, 2, 6, 9, 9, 5, 2, 9, 4, 2, 4, 6, 9, 1, 0, 9, 8, 4, 3, 4, 0, 8, 1, 1, 9, 3, 4, 3, 6, 3, 6, 3, 6, 8, 1, 1, 0, 9, 8
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OFFSET
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0,1
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COMMENTS
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Named after the German mathematician Carl Friedrich Gauss (1777-1855), the Russian mathematician Rodion Kuzmin (1891-1949) and the German mathematician Eduard Wirsing (1931-2022). - Amiram Eldar, May 29 2021
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REFERENCES
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Tim Bedford, Michael Keane and Caroline Series, eds., Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Oxford, 1991, esp. p. 204.
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 151-156.
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LINKS
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Hervé Daudé, Philippe Flajolet and Brigitte Vallée, An analysis of the Gaussian algorithm for lattice reduction, in: L. M. Adleman and M. D. Huang (eds.), Algorithmic Number Theory, First International Symposium, ANTS-I Ithaca, NY, USA, May 6-9, 1994, Proceedings, Lecture Notes in Computer Science, Vol. 877, Springer, Berlin, Heidelberg, 1994, pp. 144-158; Inria preprint.
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EXAMPLE
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0.303663002898732658597448121901...
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MATHEMATICA
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m[j_ , k_] := m[j, k] = ((-1)^j/(j!*(-2)^k))* Sum[Binomial[k, i]*(-2)^i*Pochhammer[i+2, j]* (Zeta[i+j+2]*(2^(i+j+2) - 1) - 2^(i+j+2)), {i, 0, k}] // N[#, 120]&; n = 230; $MaxExtraPrecision = 300; t = Table[m[j, k] , {j, 0, n-1}, {k, 0, n-1}] ; g = (Sort @ Abs @ Eigenvalues[t])[[-2]]; RealDigits[g, 10, 105] // First (* Jean-François Alcover, Jun 29 2011, after MathWorld *)
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PROG
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(PARI) { default(realprecision, 382); lambda=0.\
30366300289873265859744812190155623311087735225365\
78951882454814672269952942469109843408119343636368\
11098272263710616938474614859745801316065265381818\
23787913244613989647642974095044629375949048702977\
28772511058335175922044472408659119650778105589295\
79186714752925653642591844121784234492057255294269\
10040657788006767324303643964013896927671340737822\
86711534915435462112848419717968; x=10*lambda; for (n=0, 381, d=floor(x); x=(x-d)*10; write("b038517.txt", n, " ", d)); } \\ Harry J. Smith, May 13 2009
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Corrected errors in sequence using the b-file. - N. J. A. Sloane, Aug 30 2009
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STATUS
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approved
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