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.
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, 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, 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
Offset: 0
Examples
0.0095819302678393175490232932107784387586944952973855161571352169358207361...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric constants, p. 222.
Crossrefs
Cf. A242402(theta).
Programs
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Mathematica
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]
Formula
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.