A244263 Decimal expansion of beta = 1.07869..., the best constant in Friedrichs' inequality in one dimension.

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

Offset

1,3

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric Constants, p. 223.

Links

Table of n, a(n) for n=1..100.

J. T. Marti, The Least Constant in Friedrichs’ Inequality in One Dimension.

Formula

Beta = sqrt(1 + 1/theta^2), where theta is the unique solution of the equation cos(t) - t/(t^2 + 1)*sin(t) = -1, with 0 < t < Pi,

Example

1.078690216254686508024283349747...

Mathematica

theta = t /. FindRoot[Cos[t] - t/(t^2 + 1)*Sin[t] == -1, {t, 2}, WorkingPrecision -> 99]; beta = Sqrt[1 + 1/theta^2]; RealDigits[beta] // First

Crossrefs

Cf. A244262.

Sequence in context: A093827 A245736 A088660 * A288023 A020506 A193345

Adjacent sequences: A244260 A244261 A244262 * A244264 A244265 A244266

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 24 2014

Status

approved