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

Author

Jean-François Alcover, Oct 23 2014

Keywords

• nonn
• cons
• easy

Examples

			0.435345066268971927532148125596320824348...
		

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]

Crossrefs

Cf. A249205, A249206.

Programs

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

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...