cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

Views

Author

Ilya Gutkovskiy, Jun 21 2019

Keywords

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

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 + ...)))))))))).

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

Views

Author

Ilya Gutkovskiy, Jun 21 2019

Keywords

Examples

			0.45554452608187355662518203623334796282748850507693...

Links

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)

A308741 Decimal expansion of BesselI(1/4,1/2)/BesselI(-3/4,1/2).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Jun 21 2019

Keywords

Examples

			0.83633853120129660076367279911746782943585...

Links

Crossrefs

Cf. A016813 (continued fraction), A298242, A308739, A308740, A308742, A308743, A308744.

Programs

  • Mathematica
    RealDigits[BesselI[1/4, 1/2]/BesselI[-3/4, 1/2], 10, 109] [[1]]
  • PARI
    besseli(1/4,1/2)/besseli(-3/4,1/2) \\ Charles R Greathouse IV, Oct 23 2023

Formula

Equals 1/(1 + 1/(5 + 1/(9 + 1/(13 + 1/(17 + 1/(21 + 1/(25 + 1/(29 + 1/(33 + 1/(37 + ...)))))))))).

A308743 Decimal expansion of BesselI(1/5,2/5)/BesselI(-4/5,2/5).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Jun 21 2019

Keywords

Examples

			0.858964173516036374075328952007099194273985...

Links

Crossrefs

Cf. A016861 (continued fraction), A298243, A308739, A308740, A308741, A308742, A308744.

Programs

  • Mathematica
    RealDigits[BesselI[1/5, 2/5]/BesselI[-4/5, 2/5], 10, 110] [[1]]
  • PARI
    besseli(1/5,2/5)/besseli(-4/5,2/5) \\ Charles R Greathouse IV, Oct 23 2023

Formula

Equals 1/(1 + 1/(6 + 1/(11 + 1/(16 + 1/(21 + 1/(26 + 1/(31 + 1/(36 + 1/(41 + 1/(46 + ...)))))))))).

A308744 Decimal expansion of BesselI(4/5,2/5)/BesselI(-1/5,2/5).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Jun 21 2019

Keywords

Examples

			0.243294827139166639772995236321092015464991132...

Links

Crossrefs

Cf. A016897 (continued fraction), A298243, A308739, A308740, A308741, A308742, A308743.

Programs

  • Mathematica
    RealDigits[BesselI[4/5, 2/5]/BesselI[-1/5, 2/5], 10, 110] [[1]]
  • PARI
    besseli(4/5,2/5)/besseli(-1/5,2/5) \\ Charles R Greathouse IV, Oct 23 2023

Formula

Equals 1/(4 + 1/(9 + 1/(14 + 1/(19 + 1/(24 + 1/(29 + 1/(34 + 1/(39 + 1/(44 + 1/(49 + ...)))))))))).
Showing 1-5 of 5 results.

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