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 A244382 Decimal expansion of the best-known upper bound (as given by Julian Gevirtz) of the John constant for the unit disk. 1
 7, 1, 8, 7, 9, 0, 3, 3, 5, 1, 6, 4, 1, 0, 6, 2, 2, 9, 4, 4, 0, 5, 1, 1, 7, 5, 4, 9, 2, 4, 4, 4, 2, 1, 0, 6, 7, 5, 4, 5, 7, 8, 4, 1, 8, 5, 4, 1, 5, 4, 2, 8, 7, 5, 4, 9, 5, 8, 0, 6, 6, 6, 3, 7, 2, 8, 2, 0, 0, 5, 2, 6, 6, 4, 4, 0, 0, 9, 4, 0, 6, 7, 4, 3, 4, 9, 5, 0, 8, 8, 5, 5, 8, 5, 3, 8, 8, 2, 7, 4, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 7.4 John Constant, p. 466. LINKS Julian Gevirtz, An upper bound for the John constant. FORMULA exp(lambda*Pi), where lambda is the positive solution of the equation Pi/(exp(2*Pi*lambda)-1) = Sum_{k > 0} k/(k^2+lambda^2)*exp(-k*(Pi/(2*lambda))). EXAMPLE 7.187903351641062294405117549244421... 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[Exp[lambda*Pi]] // First RealDigits[N[E^(Pi Root[{(E^(2 Pi #) - 1) Beta[E^(-Pi/(2 #)), 1 - I #, -1] + (E^(2 Pi #) - 1) Beta[ E^(-Pi/(2 #)), 1 + I #, -1] + 2 Pi # &, 0.6278342676872}]), 100] // Chop][[1]] // Most (* Eric W. Weisstein, Dec 08 2017 *) CROSSREFS Cf. A244381 (lambda). Sequence in context: A199439 A153625 A011100 * A111293 A019661 A200130 Adjacent sequences: A244379 A244380 A244381 * A244383 A244384 A244385 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Jun 27 2014 STATUS approved

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Last modified December 1 15:30 EST 2022. Contains 358468 sequences. (Running on oeis4.)