A298241 -id:A298241 - cp's OEIS frontend

A298242 Decimal expansion of BesselI(1,1/2)/BesselI(0,1/2).

2, 4, 2, 4, 9, 9, 6, 1, 2, 5, 8, 0, 8, 0, 1, 9, 4, 5, 3, 5, 0, 7, 0, 2, 3, 5, 3, 5, 0, 3, 6, 3, 5, 4, 0, 7, 4, 1, 2, 2, 6, 6, 0, 4, 4, 8, 6, 5, 9, 4, 5, 5, 9, 6, 6, 7, 2, 5, 5, 8, 9, 4, 4, 7, 5, 6, 3, 9, 4, 6, 3, 3, 9, 8, 1, 3, 8, 3, 1, 0, 5, 8, 2, 6, 0, 3, 1, 7, 1, 1, 5, 1, 4, 4, 6, 7, 5, 1, 1, 0, 1, 2, 7, 6, 7, 9, 8, 5, 0, 7

Offset: 0

Ilya Gutkovskiy, Jan 15 2018

			0.2424996125808019453507023535036354074122660448659455966...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Continued Fraction Constants
Index entries for sequences related to Bessel functions or polynomials

Cf. A008586, A052119, A073744, A073747, A073821, A296168, A298241, A298243.

RealDigits[BesselI[1, 1/2]/BesselI[0, 1/2], 10, 110] [[1]]
RealDigits[Hypergeometric0F1[2, (1/2)^2/4]/(4 Gamma[2] Hypergeometric0F1[1, (1/2)^2/4]), 10, 110][[1]]

besseli(1,1/2)/besseli(0,1/2) \\ Michel Marcus, Jul 03 2018

Equals 1/(4 + 1/(8 + 1/(12 + 1/(16 + 1/(20 + 1/(24 + ...)))))).

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Jun 21 2019

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)

			0.8054800223869180458735566274757864104391314464...

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

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

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

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

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Jun 21 2019

			0.45554452608187355662518203623334796282748850507693...

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

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

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

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)

A298243 Decimal expansion of BesselI(1,2/5)/BesselI(0,2/5).

Original entry on oeis.org

1, 9, 6, 1, 0, 3, 8, 1, 2, 2, 1, 7, 9, 9, 5, 5, 1, 3, 4, 0, 8, 3, 6, 1, 0, 6, 4, 6, 2, 6, 8, 7, 8, 5, 1, 7, 3, 7, 2, 5, 0, 5, 8, 0, 9, 4, 4, 6, 4, 2, 7, 0, 0, 2, 1, 1, 7, 6, 1, 7, 1, 4, 6, 5, 6, 6, 4, 7, 2, 0, 7, 2, 4, 6, 8, 6, 9, 5, 0, 7, 4, 4, 7, 5, 7, 5, 2, 4, 7, 4, 2, 7, 1, 4, 1, 2, 4, 4, 5, 3, 3, 2, 1, 3, 0, 7, 2, 0, 4, 4

Offset: 0

Ilya Gutkovskiy, Jan 15 2018

			0.1961038122179955134083610646268785173725058094464270021...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Continued Fraction Constants
Index entries for sequences related to Bessel functions or polynomials

Cf. A008587, A052119, A073744, A073747, A073821, A296168, A298241, A298242.

RealDigits[BesselI[1, 2/5]/BesselI[0, 2/5], 10, 110] [[1]]
RealDigits[Hypergeometric0F1[2, (2/5)^2/4]/(5 Gamma[2] Hypergeometric0F1[1, (2/5)^2/4]), 10, 110][[1]]

besseli(1,2/5)/besseli(0,2/5) \\ Michel Marcus, Jul 03 2018

Equals 1/(5 + 1/(10 + 1/(15 + 1/(20 + 1/(25 + 1/(30 + ...)))))).

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A298242 Decimal expansion of BesselI(1,1/2)/BesselI(0,1/2).

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

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

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A298243 Decimal expansion of BesselI(1,2/5)/BesselI(0,2/5).

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