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A244263 Decimal expansion of beta = 1.07869..., the best constant in Friedrichs' inequality in one dimension. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,3
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric Constants, p. 223.
LINKS
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
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

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Last modified March 29 05:28 EDT 2024. Contains 371264 sequences. (Running on oeis4.)