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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. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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-Fran├žois Alcover, Jun 26 2014

STATUS

approved

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Last modified August 3 10:43 EDT 2021. Contains 346435 sequences. (Running on oeis4.)