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A248916
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Decimal expansion of gamma = 8*lambda^2, a critical threshold of a boundary value problem, where lambda is Laplace's limit constant A033259.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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]
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.8 Laplace limit constant, p. 266.
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LINKS
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EXAMPLE
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3.5138307191251612062078370932388235871...
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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