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A249220
Decimal expansion of a constant related to the [dimensionless] electrical capacitance of the ring torus without hole (with unit circle radius).
2
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
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.9 Integer Chebyshev constants, p. 268.
LINKS
Steven Finch, Electrical capacitance [Cached copy, with permission of the author]
FORMULA
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...
EXAMPLE
0.435345066268971927532148125596320824348...
MAPLE
evalf(int(1/BesselI(0, x)^2, x=0..infinity)/Pi, 50); # Vaclav Kotesovec, Oct 23 2014
MATHEMATICA
k = (1/Pi)*NIntegrate[1/BesselI[0, t]^2, {t, 0, Infinity}, WorkingPrecision -> 100]; RealDigits[k] // First
CROSSREFS
Sequence in context: A011206 A326768 A328237 * A075128 A074091 A177033
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved