A249220 - OEIS

%I #10 Jun 01 2017 14:49:12

%S 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,

%T 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,

%U 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

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

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.9 Integer Chebyshev constants, p. 268.

%H Steven Finch, <a href="/A249205/a249205.pdf">Electrical capacitance</a> [Cached copy, with permission of the author]

%F 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.

%F The electrical capacitance is 4*k = 1.74138...

%e 0.435345066268971927532148125596320824348...

%p evalf(int(1/BesselI(0,x)^2, x=0..infinity)/Pi, 50); # _Vaclav Kotesovec_, Oct 23 2014

%t k = (1/Pi)*NIntegrate[1/BesselI[0, t]^2, {t, 0, Infinity}, WorkingPrecision -> 100]; RealDigits[k] // First

%Y Cf. A249205, A249206.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Oct 23 2014