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A244354
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Decimal expansion of 'mu', 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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3
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1, 7, 2, 9, 1, 5, 0, 6, 9, 0, 3, 0, 6, 4, 4, 9, 2, 6, 9, 1, 8, 8, 6, 6, 8, 3, 4, 4, 3, 0, 1, 0, 3, 7, 1, 4, 9, 0, 2, 0, 0, 6, 7, 1, 1, 5, 9, 2, 8, 3, 9, 2, 2, 5, 6, 4, 6, 0, 6, 8, 0, 8, 4, 8, 2, 9, 4, 8, 1, 0, 6, 3, 1, 6, 3, 1, 5, 6, 3, 9, 9, 8, 8, 7, 3, 2, 4, 4, 0, 0, 9, 0, 1, 8, 3, 5, 8, 9, 5, 1, 8, 2, 2, 5
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OFFSET
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0,2
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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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mu = 1/theta^2, where theta is A115368, the first positive zero of the Bessel function J0(x).
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EXAMPLE
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0.17291506903064492691886683443...
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MATHEMATICA
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theta = BesselJZero[0, 1]; mu = 1/theta^2; RealDigits[mu, 10, 104] // First
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PROG
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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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