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
KEYWORD
AUTHOR
Jean-François Alcover, Oct 23 2014
STATUS
approved