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
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
KEYWORD
AUTHOR
Jean-François Alcover, Oct 16 2014
STATUS
approved