A249136 Decimal expansion of the largest constant 'beta' for which there exists a solution to the differential equation y''(x)+exp(y(x))=0, with y(0)=y(beta)=0.
1, 8, 7, 4, 5, 2, 1, 4, 6, 4, 0, 3, 4, 2, 6, 4, 1, 8, 7, 6, 0, 0, 3, 2, 4, 8, 2, 0, 4, 7, 0, 2, 6, 4, 1, 2, 0, 1, 4, 7, 2, 1, 9, 3, 9, 8, 9, 1, 7, 0, 5, 6, 0, 7, 4, 6, 8, 3, 7, 8, 2, 4, 8, 9, 3, 1, 6, 2, 7, 1, 0, 4, 4, 4, 7, 1, 4, 7, 3, 1, 3, 8, 8, 2, 8, 5, 6, 6, 0, 1, 8, 7, 6, 8, 7, 4, 5, 8, 2, 8, 9, 6
Offset: 1
Examples
1.874521464034264187600324820470264120147219398917056...
Links
- G. C. Greubel, Table of n, a(n) for n = 1..10000
- Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2024, p. 32.
- Eric Weisstein's MathWorld, Laplace Limit.
Programs
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Mathematica
lambda = x /. FindRoot[x*Exp[Sqrt[1 + x^2]]/(1 + Sqrt[1 + x^2]) == 1, {x, 1}, WorkingPrecision -> 102]; beta = Sqrt[8]*lambda; RealDigits[beta] // First
Formula
beta = sqrt(8)*lambda, where lambda is A033259, the Laplace limit constant 0.66274...
Equals sqrt(A248916). - Hugo Pfoertner, Dec 19 2024