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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
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 7.4 John Constant, p. 467.
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 A368669
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved