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A249220
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Decimal expansion of a constant related to the [dimensionless] electrical capacitance of the ring torus without hole (with unit circle radius).
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2
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4, 3, 5, 3, 4, 5, 0, 6, 6, 2, 6, 8, 9, 7, 1, 9, 2, 7, 5, 3, 2, 1, 4, 8, 1, 2, 5, 5, 9, 6, 3, 2, 0, 8, 2, 4, 3, 4, 8, 0, 9, 1, 5, 5, 6, 2, 7, 6, 7, 4, 5, 4, 3, 3, 6, 4, 4, 4, 6, 7, 7, 1, 6, 3, 4, 0, 9, 9, 2, 9, 3, 7, 7, 2, 4, 2, 7, 7, 7, 6, 8, 4, 2, 1, 5, 8, 1, 7, 1, 1, 3, 4, 5, 7, 9, 1, 5, 9, 5, 3
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.9 Integer Chebyshev constants, p. 268.
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LINKS
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FORMULA
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k = (1/Pi)*integral_{0..infinity} 1/I_0(t)^2 dt, where I_0 is the zeroth modified Bessel function of the first kind.
The electrical capacitance is 4*k = 1.74138...
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EXAMPLE
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0.435345066268971927532148125596320824348...
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MAPLE
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evalf(int(1/BesselI(0, x)^2, x=0..infinity)/Pi, 50); # Vaclav Kotesovec, Oct 23 2014
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MATHEMATICA
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k = (1/Pi)*NIntegrate[1/BesselI[0, t]^2, {t, 0, Infinity}, WorkingPrecision -> 100]; RealDigits[k] // First
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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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