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A244355
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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.
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2
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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
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OFFSET
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1,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.6 Sobolev Isoperimetric Constants, p. 221.
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LINKS
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FORMULA
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lambda = theta^2 where theta is A115368, the first positive zero of the Bessel function J0(x).
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.
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EXAMPLE
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5.7831859629467845211759957584558...
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MATHEMATICA
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theta = BesselJZero[0, 1]; lambda = theta^2; RealDigits[lambda, 10, 103] // First
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PROG
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(PARI) solve(x=2, 3, besselj(0, x))^2 \\ Michel Marcus, Nov 02 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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