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A244381
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Decimal expansion of 'lambda', a constant such that exp(lambda*Pi) is the best-known upper bound (as given by Julian Gevirtz) of the John constant for the unit disk.
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1
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6, 2, 7, 8, 3, 4, 2, 6, 7, 6, 8, 7, 2, 1, 3, 1, 6, 8, 2, 8, 3, 8, 3, 0, 5, 6, 6, 2, 9, 2, 4, 8, 8, 6, 8, 7, 6, 4, 5, 1, 8, 7, 3, 4, 2, 4, 3, 4, 9, 3, 9, 4, 3, 4, 3, 4, 3, 8, 4, 3, 5, 1, 5, 1, 9, 7, 3, 6, 0, 9, 1, 2, 2, 1, 9, 4, 9, 0, 6, 3, 6, 6, 6, 5, 7, 2, 2, 9, 8, 4, 2, 7, 8, 6, 8, 1, 5, 0, 2, 2, 7, 9
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 7.4 John Constant, p. 467.
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LINKS
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Table of n, a(n) for n=0..101.
Julian Gevirtz, An upper bound for the John constant.
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FORMULA
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Positive solution of the equation Pi/(exp(2*Pi*lambda)-1) = sum_(k=1..infinity) k/(k^2+lambda^2)*exp(-k*(Pi/(2*lambda))).
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EXAMPLE
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0.62783426768721316828383...
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MATHEMATICA
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eq = Pi/(Exp[2*Pi*x] - 1) == Sum[(k/(k^2 + x^2))*Exp[-k*(Pi/(2*x))], {k, 1, Infinity}]; lambda = x /. FindRoot[eq, {x, 1/2}, WorkingPrecision -> 102] // Re; RealDigits[lambda] // First
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CROSSREFS
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Cf. A244382.
Sequence in context: A115731 A163340 A326823 * A307086 A021090 A270138
Adjacent sequences: A244378 A244379 A244380 * A244382 A244383 A244384
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KEYWORD
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nonn,cons,easy
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AUTHOR
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Jean-François Alcover, Jun 27 2014
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STATUS
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approved
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