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

0,3

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric constants, p. 222.

Links

Table of n, a(n) for n=0..100.

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.

Example

0.0095819302678393175490232932107784387586944952973855161571352169358207361...

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]

Crossrefs

Cf. A242402(theta).

Sequence in context: A117019 A155692 A011203 * A203081 A346440 A329715

Adjacent sequences: A245289 A245290 A245291 * A245293 A245294 A245295

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 17 2014

Status

approved