A244263 - OEIS

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

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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...