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Decimal expansion of Gauss-Kuzmin-Wirsing constant.
5

%I #49 Oct 02 2023 02:40:41

%S 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,

%T 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,

%U 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

%N Decimal expansion of Gauss-Kuzmin-Wirsing constant.

%C 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

%D Tim Bedford, Michael Keane and Caroline Series, eds., Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Oxford, 1991, esp. p. 204.

%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 151-156.

%H Harry J. Smith, <a href="/A038517/b038517.txt">Table of n, a(n) for n = 0..381</a>

%H Keith Briggs, <a href="http://keithbriggs.info/documents/wirsing.pdf">A precise computation of the Gauss-Kuzmin-Wirsing constant</a>, 2003.

%H Hervé Daudé, Philippe Flajolet and Brigitte Vallée, <a href="https://doi.org/10.1007/3-540-58691-1_52">An analysis of the Gaussian algorithm for lattice reduction</a>, 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; <a href="https://hal.inria.fr/inria-00074428/">Inria preprint</a>.

%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/kuzmin/kuzmin.html">The Gauss-Kuzmin-Wirsing Constant</a>. [Broken link]

%H Steven R. Finch, <a href="http://web.archive.org/web/20010603070928/http://www.mathsoft.com/asolve/constant/kuzmin/kuzmin.html">The Gauss-Kuzmin-Wirsing Constant</a>. [From the Wayback machine]

%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap45.html">The Gauss-Kuzmin-Wirsing constant</a>.

%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/gkw.txt">The Gauss-Kuzmin-Wirsing constant</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Gauss-Kuzmin-WirsingConstant.html">Kuzmin-Wirsing Constant</a>.

%e 0.303663002898732658597448121901...

%t 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 *)

%o (PARI) { default(realprecision,382); lambda=0.\

%o 30366300289873265859744812190155623311087735225365\

%o 78951882454814672269952942469109843408119343636368\

%o 11098272263710616938474614859745801316065265381818\

%o 23787913244613989647642974095044629375949048702977\

%o 28772511058335175922044472408659119650778105589295\

%o 79186714752925653642591844121784234492057255294269\

%o 10040657788006767324303643964013896927671340737822\

%o 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

%Y Cf. A007515.

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Robert G. Wilson v_, Aug 03 2002

%E Extended by _Eric W. Weisstein_ using a computation of _Keith Briggs_, Jul 08 2003

%E Corrected errors in sequence using the b-file. - _N. J. A. Sloane_, Aug 30 2009