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%I #5 Jun 26 2014 12:55:03
%S 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,
%T 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,
%U 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
%N 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.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric Constants, p. 221.
%F lambda = theta^4/Pi^4 = 1/(Pi^4*mu), where theta is A076414 and mu is A244347.
%F lambda is also the smallest eigenvalue of the ODE g''''(x)=lambda*g(x), g(0)=g'(0)=g(Pi)=g'(Pi)=0.
%e 5.13878013260283423689422...
%t 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
%Y Cf. A076414 (theta), A244347 (mu).
%K nonn,cons,easy
%O 1,1
%A _Jean-François Alcover_, Jun 26 2014
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