A038517 - OEIS

A038517

Decimal expansion of Gauss-Kuzmin-Wirsing constant.

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

COMMENTS

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

REFERENCES

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.

LINKS

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

Keith Briggs, A precise computation of the Gauss-Kuzmin-Wirsing constant, 2003.

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.

Steven R. Finch, The Gauss-Kuzmin-Wirsing Constant. [Broken link]

Steven R. Finch, The Gauss-Kuzmin-Wirsing Constant. [From the Wayback machine]

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-François 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)); } \\ Harry J. Smith, May 13 2009

CROSSREFS

Cf. A007515.

Sequence in context: A247734 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, Jul 08 2003

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

STATUS

approved