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

Author

Jean-François Alcover, Jun 24 2014

Keywords

• nonn
• cons
• easy

Examples

			1.078690216254686508024283349747...
		

References

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

Links

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

Crossrefs

Cf. A244262.

Programs

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,