A249137 Decimal expansion of the derivative y'(0) where y(x) is the solution to the differential equation y''(x)+exp(y(x))=0, with y(0)=y(beta)=0 and beta maximum (beta = A249136).

2, 1, 3, 3, 8, 7, 7, 9, 3, 9, 9, 1, 5, 0, 6, 1, 1, 1, 9, 8, 0, 7, 2, 4, 4, 6, 7, 7, 4, 0, 1, 8, 5, 2, 9, 1, 9, 2, 2, 8, 9, 6, 2, 3, 8, 5, 3, 7, 9, 6, 4, 6, 8, 6, 1, 7, 7, 7, 2, 3, 4, 5, 9, 2, 7, 1, 9, 0, 6, 1, 1, 7, 5, 5, 7, 7, 4, 9, 9, 0, 3, 8, 1, 5, 7, 5, 2, 3, 9, 9, 3, 3, 7, 4, 7, 3, 2, 9, 4, 3, 3, 5, 6

Offset

1,1

Links

Table of n, a(n) for n=1..103.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 32.

Eric Weisstein's MathWorld, Laplace Limit.

Formula

y'(0) = sqrt(2)*sinh(sqrt(lambda^2 + 1)), where lambda is A033259, the Laplace limit constant 0.66274...

Example

2.13387793991506111980724467740185291922896238537964686...

Mathematica

digits = 103; lambda = x /. FindRoot[x*Exp[Sqrt[1 + x^2]]/(1 + Sqrt[1 + x^2]) == 1, {x, 1}, WorkingPrecision -> digits+5]; mu = Sqrt[lambda^2 + 1]; RealDigits[Sqrt[2]*Sinh[mu], 10, digits] // First

Crossrefs

Cf. A033259, A085984, A248916, A249136.

Sequence in context: A183256 A328319 A307366 * A246174 A176054 A257703

Adjacent sequences: A249134 A249135 A249136 * A249138 A249139 A249140

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Oct 22 2014

Status

approved