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.

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.

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 A368669

Adjacent sequences: A244378 A244379 A244380 * A244382 A244383 A244384

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 27 2014

Status

approved