

A244381


Decimal expansion of 'lambda', a constant such that exp(lambda*Pi) is the bestknown 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
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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

JeanFrançois Alcover, Jun 27 2014


STATUS

approved



