A249220 Decimal expansion of a constant related to the [dimensionless] electrical capacitance of the ring torus without hole (with unit circle radius).

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

Table of n, a(n) for n=0..99.

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

Cf. A249205, A249206.

Sequence in context: A011206 A326768 A328237 * A075128 A074091 A177033

Adjacent sequences: A249217 A249218 A249219 * A249221 A249222 A249223

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Oct 23 2014

Status

approved