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)
LINKS
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
KEYWORD
nonn,cons
AUTHOR
Ilya Gutkovskiy, Jun 21 2019
STATUS
approved