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
Examples
1.078690216254686508024283349747...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric Constants, p. 223.
Links
Crossrefs
Cf. A244262.
Programs
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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
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,