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

Author

Jean-François Alcover, Jun 26 2014

Keywords

• nonn
• cons
• easy

Examples

			5.13878013260283423689422...
		

References

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

Crossrefs

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

Programs

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

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.