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A038517 Decimal expansion of Gauss-Kuzmin-Wirsing constant. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

T. Bedford et al., eds., Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Oxford, 1991, esp. p. 204.

H. Daude, P. Flajolet and B. Vallee, An average-case analysis of the Gaussian algorithm for lattice reduction, INRIA, 1996.

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 151-156.

LINKS

Harry J. Smith, Table of n, a(n) for n=0,...,381

Keith Briggs, A precise computation of the Gauss-Kuzmin-Wirsing constant

H. Daude, P. Flajolet and B. Vallee, An average-case analysis of the Gaussian algorithm for lattice reduction, INRIA, 1996.

S. R. Finch, The Gauss-Kuzmin-Wirsing Constant

Simon Plouffe, The Gauss-Kuzmin-Wirsing constant

Simon Plouffe, The Gauss-Kuzmin-Wirsing constant

Eric Weisstein's World of Mathematics, Kuzmin-Wirsing Constant

EXAMPLE

0.303663002898732658597448121901...

MATHEMATICA

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-Fran├žois Alcover, Jun 29 2011, after MathWorld *)

PROG

(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)); } [From Harry J. Smith, May 13 2009]

CROSSREFS

Cf. A007515.

Sequence in context: A200278 A010599 A226568 * A055949 A165012 A198126

Adjacent sequences:  A038514 A038515 A038516 * A038518 A038519 A038520

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Robert G. Wilson v, Aug 03 2002

Extended by Eric W. Weisstein using a computation of Keith Briggs (keith.briggs(AT)bt.com), Jul 08, 2003

Fixed my PARI program, had -n Harry J. Smith, May 19 2009

Corrected errors in sequence using the b-file. - N. J. A. Sloane, Aug 30 2009

STATUS

approved

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Last modified August 1 02:02 EDT 2014. Contains 245104 sequences.