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%I #39 Jul 09 2023 02:52:41
%S 1,2,6,6,0,6,5,8,7,7,7,5,2,0,0,8,3,3,5,5,9,8,2,4,4,6,2,5,2,1,4,7,1,7,
%T 5,3,7,6,0,7,6,7,0,3,1,1,3,5,4,9,6,2,2,0,6,8,0,8,1,3,5,3,3,1,2,1,3,5,
%U 7,5,0,1,6,1,2,2,7,7,5,4,7,0,3,9,4,8,1,8,3,5,7,1,4,7,2,8,0,1,0,1,8,7,1,0,3,6,1,3,4,6,8
%N Decimal expansion of the Modified Bessel Function I of order 0 at 1.
%H M. Abramowitz and I. A. Stegun, <a href="http://people.math.sfu.ca/~cbm/aands/page_374.htm">Handbook of Mathematical functions</a>, Chapter 9.6.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html">Modified Bessel Function of the First Kind</a>.
%F I_0(1) = Sum_{k>=0} 1/(4^k*k!^2) = Sum_{k>=0} 1/A002454(k).
%F Equals (1/Pi)*Integral_{t=0..Pi} exp(cos(t)) dt.
%F Equals BesselJ(0,i). - _Jianing Song_, Sep 18 2021
%F From _Amiram Eldar_, Jul 09 2023: (Start)
%F Equals exp(-1) * Sum_{k>=0} binomial(2*k,k)/(2^k*k!).
%F Equals e * Sum_{k>=0} (-1/2)^k * binomial(2*k,k)/k!. (End)
%e 1.26606587775200833559824462521471753760767031135496...
%p BesselI(0,1) ;evalf(%) ;
%t RealDigits[BesselJ[0, I], 10, 120][[1]] (* _Amiram Eldar_, Jun 15 2023 *)
%o (PARI) besseli(0,1) \\ _Charles R Greathouse IV_, Feb 19 2014
%Y Cf. A002454, A242282.
%Y Bessel function values: A334380 (J(0,1)), A334383 (J(0,sqrt(2)), A091681 (J(0,2)), this sequence (I(0,1)), A334381 (I(0,sqrt(2)), A070910 (I(0,2)).
%K cons,easy,nonn
%O 1,2
%A _R. J. Mathar_, Oct 08 2011
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