A248916 Decimal expansion of gamma = 8*lambda^2, a critical threshold of a boundary value problem, where lambda is Laplace's limit constant A033259.

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

Offset: 1

Author

Jean-François Alcover, Oct 16 2014

Keywords

• nonn
• cons
• easy

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]

Examples

			3.5138307191251612062078370932388235871...
		

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..20000
• Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 32.
• Eric Weisstein's MathWorld, Laplace Limit

Crossrefs

Cf. A033259, A085984.

Programs

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