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%I #17 Aug 09 2022 04:21:31
%S 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,
%T 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,
%U 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
%N 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.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric Constants, p. 221.
%H Robert Stephen Jones, <a href="https://arxiv.org/abs/1712.06082">The fundamental Laplacian eigenvalue of the regular polygon with Dirichlet boundary conditions</a>, arXiv:1712.06082 [math.NA], 2017, p. 17.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/BesselFunctionZeros.html">Bessel Function Zeros</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F lambda = theta^2 where theta is A115368, the first positive zero of the Bessel function J0(x).
%F lambda = 1/mu = 1/A244354.
%F 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.
%e 5.7831859629467845211759957584558...
%t theta = BesselJZero[0, 1]; lambda = theta^2; RealDigits[lambda, 10, 103] // First
%o (PARI) solve(x=2, 3, besselj(0, x))^2 \\ _Michel Marcus_, Nov 02 2018
%o (PARI) besseljzero(0)^2 \\ _Charles R Greathouse IV_, Aug 09 2022
%Y Cf. A115368, A244354.
%K nonn,cons,easy
%O 1,1
%A _Jean-François Alcover_, Jun 26 2014
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