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A244381 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. 1
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; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 7.4 John Constant, p. 467.

LINKS

Table of n, a(n) for n=0..101.

Julian Gevirtz, An upper bound for the John constant.

FORMULA

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))).

EXAMPLE

0.62783426768721316828383...

MATHEMATICA

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

CROSSREFS

Cf. A244382.

Sequence in context: A115731 A163340 A326823 * A307086 A021090 A270138

Adjacent sequences: A244378 A244379 A244380 * A244382 A244383 A244384

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Jun 27 2014

STATUS

approved

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Last modified December 9 11:21 EST 2022. Contains 358700 sequences. (Running on oeis4.)