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A308739
Decimal expansion of BesselI(1/3,2/3)/BesselI(-2/3,2/3).
6
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, 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, 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
OFFSET
0,1
COMMENTS
From Peter Bala, Nov 28 2019: (Start)
Denoting this constant by c, we have the related simple continued fraction expansions:
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, ...];
(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)
FORMULA
Equals 1/(1 + 1/(4 + 1/(7 + 1/(10 + 1/(13 + 1/(16 + 1/(19 + 1/(22 + 1/(25 + 1/(28 + ...)))))))))).
EXAMPLE
0.8054800223869180458735566274757864104391314464...
MATHEMATICA
RealDigits[BesselI[1/3, 2/3]/BesselI[-2/3, 2/3], 10, 110] [[1]]
PROG
(PARI) besseli(1/3, 2/3)/besseli(-2/3, 2/3) \\ Felix Fröhlich, Dec 01 2019
CROSSREFS
Cf. A016777 (continued fraction), A073744, A298241, A308740, A308741, A308742, A308743, A308744.
Sequence in context: A096152 A021558 A335958 * A118253 A135001 A146293
KEYWORD
nonn,cons
AUTHOR
Ilya Gutkovskiy, Jun 21 2019
STATUS
approved