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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.

%I A249136 #22 Feb 16 2025 08:33:24
%S A249136 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,
%T A249136 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,
%U A249136 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
%N 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.
%H A249136 G. C. Greubel, <a href="/A249136/b249136.txt">Table of n, a(n) for n = 1..10000</a>
%H A249136 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020-2024, p. 32.
%H A249136 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/LaplaceLimit.html">Laplace Limit.</a>
%F A249136 beta = sqrt(8)*lambda, where lambda is A033259, the Laplace limit constant 0.66274...
%F A249136 Equals sqrt(A248916). - _Hugo Pfoertner_, Dec 19 2024
%e A249136 1.874521464034264187600324820470264120147219398917056...
%t A249136 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
%Y A249136 Cf. A033259, A085984, A248916.
%K A249136 nonn,cons,easy
%O A249136 1,2
%A A249136 _Jean-François Alcover_, Oct 22 2014