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%I #14 Dec 07 2019 22:09:56
%S 8,0,5,4,8,0,0,2,2,3,8,6,9,1,8,0,4,5,8,7,3,5,5,6,6,2,7,4,7,5,7,8,6,4,
%T 1,0,4,3,9,1,3,1,4,4,6,4,2,0,4,4,2,6,8,8,6,0,2,9,6,6,8,3,4,0,6,5,1,9,
%U 2,0,3,8,2,3,0,9,3,3,5,9,3,7,4,9,2,4,5,7,6,3,2,2,3,8,5,3,6,2,5,0,5,5,4,7,7,6,5,7,9,7
%N Decimal expansion of BesselI(1/3,2/3)/BesselI(-2/3,2/3).
%C From _Peter Bala_, Nov 28 2019: (Start)
%C Denoting this constant by c, we have the related simple continued fraction expansions:
%C 3*c = [2; 2, 2, 2, 30, 4, 2, 1, 4, 1, 2, 6, 66, 8, 2, 1, 8, 1, 2, 10, ..., 3*(12*k + 10), 4*k + 4, 2, 1, 4*k + 4, 1, 2, 4*k + 6, ...];
%C (1/3)*c = [0; 3, 1, 2, 1, 1, 1, 2, 3, 39, 5, 2, 1, 5, 1, 2, 7, 75, 9, 2, 1, 9, 1, 2, 11, ..., 3*(12*k + 1), 4*k + 1, 2, 1, 4*k + 1, 1, 2, 4*k + 3, ...]. (End)
%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/(1 + 1/(4 + 1/(7 + 1/(10 + 1/(13 + 1/(16 + 1/(19 + 1/(22 + 1/(25 + 1/(28 + ...)))))))))).
%e 0.8054800223869180458735566274757864104391314464...
%t RealDigits[BesselI[1/3, 2/3]/BesselI[-2/3, 2/3], 10, 110] [[1]]
%o (PARI) besseli(1/3,2/3)/besseli(-2/3,2/3) \\ _Felix Fröhlich_, Dec 01 2019
%Y Cf. A016777 (continued fraction), A073744, A298241, A308740, A308741, A308742, A308743, A308744.
%K nonn,cons
%O 0,1
%A _Ilya Gutkovskiy_, Jun 21 2019
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