cp's OEIS Frontend

A245292 Decimal expansion of 'mu', an isoperimetric constant associated with the study of a vibrating, homogeneous plate clamped at the boundary of the unit disk.

%I A245292 #9 Jul 17 2014 22:09:00
%S A245292 0,0,9,5,8,1,9,3,0,2,6,7,8,3,9,3,1,7,5,4,9,0,2,3,2,9,3,2,1,0,7,7,8,4,
%T A245292 3,8,7,5,8,6,9,4,4,9,5,2,9,7,3,8,5,5,1,6,1,5,7,1,3,5,2,1,6,9,3,5,8,2,
%U A245292 0,7,3,6,1,0,2,0,2,6,7,8,4,9,1,1,2,8,8,1,7,9,0,6,6,8,7,9,5,0,8,3,7
%N A245292 Decimal expansion of 'mu', an isoperimetric constant associated with the study of a vibrating, homogeneous plate clamped at the boundary of the unit disk.
%D A245292 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric constants, p. 222.
%F A245292 mu = 1 / theta^4, where theta is the smallest positive root of I1(t)*J0(t) + I0(t)*J1(t) = 0, with I0, I1, J0, J1, Bessel functions.
%e A245292 0.0095819302678393175490232932107784387586944952973855161571352169358207361...
%t A245292 theta = t /. FindRoot[BesselJ[0, t]*BesselI[1, t] + BesselI[0, t]*BesselJ[1, t] == 0, {t, 3}, WorkingPrecision -> 100]; mu = 1/theta^4; Join[{0, 0}, RealDigits[mu] // First]
%Y A245292 Cf. A242402(theta).
%K A245292 nonn,cons,easy
%O A245292 0,3
%A A245292 _Jean-François Alcover_, Jul 17 2014