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

1,2

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.

Formula

beta = sqrt(8)*lambda, where lambda is A033259, the Laplace limit constant 0.66274...

Equals sqrt(A248916). - Hugo Pfoertner, Dec 19 2024

Example

1.874521464034264187600324820470264120147219398917056...

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

Crossrefs

Cf. A033259, A085984, A248916.

Sequence in context: A196914 A072102 A274442 * A154815 A085848 A008960

Adjacent sequences: A249133 A249134 A249135 * A249137 A249138 A249139

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Oct 22 2014

Status

approved