A308739 Decimal expansion of BesselI(1/3,2/3)/BesselI(-2/3,2/3).

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

Author

Ilya Gutkovskiy, Jun 21 2019

Keywords

• nonn
• cons

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)

Examples

			0.8054800223869180458735566274757864104391314464...
		

Links

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

Crossrefs

Cf. A016777 (continued fraction), A073744, A298241, A308740, A308741, A308742, A308743, A308744.

Programs

Mathematica

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

PARI

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

Formula

Equals 1/(1 + 1/(4 + 1/(7 + 1/(10 + 1/(13 + 1/(16 + 1/(19 + 1/(22 + 1/(25 + 1/(28 + ...)))))))))).