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A033259 Decimal expansion of Laplace's limit constant. 11
6, 6, 2, 7, 4, 3, 4, 1, 9, 3, 4, 9, 1, 8, 1, 5, 8, 0, 9, 7, 4, 7, 4, 2, 0, 9, 7, 1, 0, 9, 2, 5, 2, 9, 0, 7, 0, 5, 6, 2, 3, 3, 5, 4, 9, 1, 1, 5, 0, 2, 2, 4, 1, 7, 5, 2, 0, 3, 9, 2, 5, 3, 4, 9, 9, 0, 9, 7, 1, 8, 5, 3, 0, 8, 6, 5, 1, 1, 2, 7, 7, 2, 4, 9, 6, 5, 4, 8, 0, 2, 5, 9, 8, 9, 5, 8, 1, 8, 1, 6, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Maximum value taken by the function x/cosh(x), which occurs at A085984. - Hrothgar, Mar 12 2014

Given two equal coaxial circular rings of diameter D located in two parallel planes distant d apart, this constant is the maximum value of d / D so that there exists a catenoid resting on these two rings. - Robert FERREOL, Feb 07 2019

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 266-268.

LINKS

Table of n, a(n) for n=0..100.

Steven R. Finch, Laplace Limit Constant [Broken link]

Steven R. Finch, Laplace Limit Constant [From the Wayback machine]

J. J. Green, The Lipschitz constant for the radial projection on real l_p - implementation notes, 2012. - N. J. A. Sloane, Sep 19 2012

Simon Plouffe, The laplace limit constant(to 500 digits)

Eric Weisstein's World of Mathematics, Laplace Limit.

Eric Weisstein's World of Mathematics, Kepler's Equation

FORMULA

Equals sqrt(A085984^2-1). [Jean-Fran├žois Alcover, May 14 2013]

EXAMPLE

0.662743419349181580974742097109252907056233549115022417520392534990971853086...

MATHEMATICA

x/.FindRoot[ x Exp[ Sqrt[ 1+x^2 ] ]/(1+Sqrt[ 1+x^2 ])==1, {x, 1} ]

Sqrt[x^2 - 1] /. FindRoot[ x == Coth[x], {x, 1}, WorkingPrecision -> 30 ]  (* Leo C. Stein, Jul 30 2017 *)

PROG

(PARI) sqrt(solve(u=1, 2, tanh(u)-1/u)^2-1)   \\ M. F. Hasler, Feb 01 2011

CROSSREFS

Cf. A033259 - A033263, A085984.

Sequence in context: A218387 A178857 A003676 * A212298 A064926 A285814

Adjacent sequences:  A033256 A033257 A033258 * A033260 A033261 A033262

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)