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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 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 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-François Alcover, Jun 26 2014 STATUS approved

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