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%I #14 Dec 07 2019 21:25:14
%S 4,5,5,5,4,4,5,2,6,0,8,1,8,7,3,5,5,6,6,2,5,1,8,2,0,3,6,2,3,3,3,4,7,9,
%T 6,2,8,2,7,4,8,8,5,0,5,0,7,6,9,3,1,7,9,9,4,5,7,5,1,6,1,2,2,9,3,0,4,5,
%U 5,0,9,2,7,7,5,6,7,3,2,1,4,5,2,0,2,1,0,6,7,5,3,5,8,2,5,2,0,2,5,7,7,9,7,6,3,9,4,7,5,7
%N Decimal expansion of BesselI(2/3,2/3)/BesselI(-1/3,2/3).
%H P. Bala, <a href="/A308739/a308739.pdf">A note on A308739 and A308740</a>
%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%F Equals 1/(2 + 1/(5 + 1/(8 + 1/(11 + 1/(14 + 1/(17 + 1/(20 + 1/(23 + 1/(26 + 1/(29 + ...)))))))))).
%F From _Peter Bala_, Nov 29 2019: (Start)
%F Denoting this constant by c, we have the related simple continued fraction expansions:
%F 3*c = [1; 2, 1, 2, 1, 2, 33, 4, 1, 2, 5, 2, 1, 6, 69, 8, 1, 2, 9, 2, 1, 10, ..., 3*(12*k + 11), 4*k + 4, 1, 2, 4*k + 5, 2, 1, 4*k + 6, ...];
%F (1/3)*c = [0; 6, 1, 1, 2, 2, 2, 1, 3, 42, 5, 1, 2, 6, 2, 1, 7, ..., 3*(12*k + 2), 4*k + 1, 1, 2, 4*k + 2, 2, 1, 4*k + 3, ...]. (End)
%e 0.45554452608187355662518203623334796282748850507693...
%t RealDigits[BesselI[2/3, 2/3]/BesselI[-1/3, 2/3], 10, 110] [[1]]
%o (PARI) besseli(2/3,2/3)/besseli(-1/3,2/3) \\ _Felix Fröhlich_, Dec 01 2019
%Y Cf. A016789 (continued fraction), A073744, A298241, A308739, A308741, A308742, A308743, A308744.
%K nonn,cons
%O 0,1
%A _Ilya Gutkovskiy_, Jun 21 2019