A244347 Decimal expansion of 'mu', a Sobolev isoperimetric constant related to the "rod inequality", arising from the elasticity study of a rod that is clamped at both ends.

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

Offset

0,4

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric Constants, p. 221.

Links

Table of n, a(n) for n=0..105.

Index entries for transcendental numbers.

Formula

mu = 1/theta^4, where theta is A076414.

Example

0.001997746934053886262....

Mathematica

digits = 104; theta = x /. FindRoot[Cos[x]*Cosh[x] == 1, {x, 5}, WorkingPrecision -> digits+10]; mu = 1/theta^4; Join[{0, 0}, RealDigits[mu, 10, digits] // First]

Prog

(PARI) solve(x=4, 5, cos(x)*cosh(x)-1)^-4 \\ Charles R Greathouse IV, May 18 2026

Crossrefs

Cf. A076414 (theta).

Sequence in context: A196399 A388362 A239528 * A388892 A341901 A144669

Adjacent sequences: A244344 A244345 A244346 * A244348 A244349 A244350

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 26 2014

Status

approved