A244350 Decimal expansion of 'lambda', a Sobolev isoperimetric constant related to the "rod inequality", arising from the elasticity study of a rod that is clamped at both ends.

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

Offset

1,1

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=1..103.

Formula

lambda = theta^4/Pi^4 = 1/(Pi^4*mu), where theta is A076414 and mu is A244347.

lambda is also the smallest eigenvalue of the ODE g''''(x)=lambda*g(x), g(0)=g'(0)=g(Pi)=g'(Pi)=0.

Example

5.13878013260283423689422...

Mathematica

digits = 103; theta = x /. FindRoot[Cos[x]*Cosh[x] == 1, {x, 5}, WorkingPrecision -> digits+10]; lambda = theta^4/Pi^4; RealDigits[lambda, 10, digits] // First

Crossrefs

Cf. A076414 (theta), A244347 (mu).

Sequence in context: A214803 A225984 A074048 * A176321 A248130 A365457

Adjacent sequences: A244347 A244348 A244349 * A244351 A244352 A244353

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 26 2014

Status

approved