A244355 Decimal expansion of 'lambda', a Sobolev isoperimetric constant related to the "membrane inequality", arising from the study of a vibrating membrane that is stretched across the unit disk and fastened at its boundary.

5, 7, 8, 3, 1, 8, 5, 9, 6, 2, 9, 4, 6, 7, 8, 4, 5, 2, 1, 1, 7, 5, 9, 9, 5, 7, 5, 8, 4, 5, 5, 8, 0, 7, 0, 3, 5, 0, 7, 1, 4, 4, 1, 8, 0, 6, 4, 2, 3, 6, 8, 5, 5, 8, 7, 0, 8, 7, 1, 2, 3, 7, 1, 4, 4, 5, 6, 0, 6, 4, 3, 0, 4, 8, 8, 5, 5, 4, 4, 3, 7, 3, 8, 8, 6, 3, 4, 0, 3, 5, 9, 5, 4, 4, 4, 9, 0, 2, 0, 4, 3, 8, 2

Offset

1,1

References

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

Links

Table of n, a(n) for n=1..103.

Robert Stephen Jones, The fundamental Laplacian eigenvalue of the regular polygon with Dirichlet boundary conditions, arXiv:1712.06082 [math.NA], 2017, p. 17.

Eric Weisstein's MathWorld, Bessel Function Zeros

Index entries for transcendental numbers

Formula

lambda = theta^2 where theta is A115368, the first positive zero of the Bessel function J0(x).

lambda = 1/mu = 1/A244354.

lambda is also the smallest eigenvalue of the ODE r^2*g''(r)+r*g'(r)+lambda*r^2*g(r)=0, g(0)=1, g(1)=0.

Example

5.7831859629467845211759957584558...

Mathematica

theta = BesselJZero[0, 1]; lambda = theta^2; RealDigits[lambda, 10, 103] // First

Prog

(PARI) solve(x=2, 3, besselj(0, x))^2 \\ Michel Marcus, Nov 02 2018
(PARI) besseljzero(0)^2 \\ Charles R Greathouse IV, Aug 09 2022

Crossrefs

Cf. A115368, A244354.

Sequence in context: A135096 A153104 A233527 * A245278 A155855 A070366

Adjacent sequences: A244352 A244353 A244354 * A244356 A244357 A244358

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 26 2014

Status

approved