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A086702
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Decimal expansion of Lévy's constant.
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14
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3, 2, 7, 5, 8, 2, 2, 9, 1, 8, 7, 2, 1, 8, 1, 1, 1, 5, 9, 7, 8, 7, 6, 8, 1, 8, 8, 2, 4, 5, 3, 8, 4, 3, 8, 6, 3, 6, 0, 8, 4, 7, 5, 5, 2, 5, 9, 8, 2, 3, 7, 4, 1, 4, 9, 4, 0, 5, 1, 9, 8, 9, 2, 4, 1, 9, 0, 7, 2, 3, 2, 1, 5, 6, 4, 4, 9, 6, 0, 3, 5, 5, 1, 8, 1, 2, 7, 7, 5, 4, 0, 4, 7, 9, 1, 7, 4, 5, 2, 9, 4, 9, 2, 6, 9
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OFFSET
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1,1
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COMMENTS
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Let P(k)/Q(k) denote the k-th convergent of x. Then for almost all irrational values of x, lim_{k->inf} Q(k)^(1/k) = L. [edited by Jared Kish, Oct 17 2014; edited by A.H.M. Smeets, Jun 26 2018]
The conditions for x, such that lim_{k->inf} Q(k)^(1/k) = L, are that the terms occurring in the continued fraction for the value of x must satisfy the Gauss-Kuzmin distribution and the terms must occur in random order in the continued fraction sequence. - A.H.M. Smeets, Jun 26 2018
Named after the French mathematician Paul Lévy (1886 - 1971). - Amiram Eldar, Sep 25 2022
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REFERENCES
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Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 59-65.
Paul Lévy, Théorie de l'addition des variables aléatoires, 2nd. ed., Editions Jacques Gabay, 1954, chap. IX, pp. 316-320.
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LINKS
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FORMULA
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L = exp(Pi^2/(12*log(2))).
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EXAMPLE
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3.27582291872181115978768...
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MATHEMATICA
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PROG
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(Magma) C<i> := ComplexField(); [Exp((Pi(C))^2/(12*Log(2)))]; // G. C. Greubel, Nov 06 2017
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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