login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..101.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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