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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.
3

%I #5 Jun 26 2014 12:54:41

%S 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,

%T 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,

%U 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

%N 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.

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

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

%e 0.001997746934053886262...

%t 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]

%Y Cf. A076414 (theta).

%K nonn,cons,easy

%O 0,4

%A _Jean-François Alcover_, Jun 26 2014