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A248916 Decimal expansion of gamma = 8*lambda^2, a critical threshold of a boundary value problem, where lambda is Laplace's limit constant A033259. 2
3, 5, 1, 3, 8, 3, 0, 7, 1, 9, 1, 2, 5, 1, 6, 1, 2, 0, 6, 2, 0, 7, 8, 3, 7, 0, 9, 3, 2, 3, 8, 8, 2, 3, 5, 8, 7, 1, 0, 9, 1, 3, 4, 2, 1, 1, 9, 5, 1, 2, 8, 4, 3, 6, 8, 1, 8, 2, 5, 4, 1, 8, 5, 2, 5, 3, 4, 9, 2, 1, 8, 6, 0, 8, 7, 7, 3, 5, 3, 0, 6, 2, 2, 4, 5, 1, 3, 9, 8, 4, 8, 8, 7, 6, 5, 9, 9, 9, 7, 5, 7, 3, 9, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The boundary value problem y''(x) + c*exp(y(x)) = 0, y(0) = y(1) = 0 and c > 0, has 0, 1 or 2 solutions when c > gamma, c = gamma and c < gamma, respectively. [After Steven Finch]

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.8 Laplace limit constant, p. 266.

LINKS

Table of n, a(n) for n=1..104.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 32.

Eric Weisstein's MathWorld, Laplace Limit

EXAMPLE

3.5138307191251612062078370932388235871...

MATHEMATICA

digits = 104; lambda = x /. FindRoot[x Exp[Sqrt[1 + x^2]]/(1 + Sqrt[1 + x^2]) == 1, {x, 1}, WorkingPrecision -> digits + 5]; gamma = 8*lambda^2; RealDigits[gamma, 10, digits] // First

CROSSREFS

Cf. A033259, A085984.

Sequence in context: A243854 A084243 A275056 * A030311 A198881 A318488

Adjacent sequences:  A248913 A248914 A248915 * A248917 A248918 A248919

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Oct 16 2014

STATUS

approved

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Last modified February 23 12:03 EST 2019. Contains 320431 sequences. (Running on oeis4.)