A308740 Decimal expansion of BesselI(2/3,2/3)/BesselI(-1/3,2/3).

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, 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, 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

Offset: 0

Author

Ilya Gutkovskiy, Jun 21 2019

Keywords

• nonn
• cons

Examples

			0.45554452608187355662518203623334796282748850507693...
		

Links

• P. Bala, A note on A308739 and A308740
• Index entries for sequences related to Bessel functions or polynomials

Crossrefs

Cf. A016789 (continued fraction), A073744, A298241, A308739, A308741, A308742, A308743, A308744.

Programs

Mathematica

RealDigits[BesselI[2/3, 2/3]/BesselI[-1/3, 2/3], 10, 110] [[1]]

PARI

besseli(2/3,2/3)/besseli(-1/3,2/3) \\ Felix Fröhlich, Dec 01 2019

Formula

Equals 1/(2 + 1/(5 + 1/(8 + 1/(11 + 1/(14 + 1/(17 + 1/(20 + 1/(23 + 1/(26 + 1/(29 + ...)))))))))).

From Peter Bala, Nov 29 2019: (Start)

Denoting this constant by c, we have the related simple continued fraction expansions:

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, ...];

(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)