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 1-3 of 3 results.

A099792 Positions of records for terms in the continued fraction of the Glaisher-Kinkelin constant A.

Original entry on oeis.org

1, 2, 5, 10, 13, 267, 3171, 3213, 12962, 82528
Offset: 1

Views

Author

Eric W. Weisstein, Oct 27 2004

Keywords

Comments

Incorrectly indexed version of A225752.

Links

Crossrefs

Cf. A225752 (= a(n) - 1).
Cf. A099791.

Formula

a(n) = A225752(n) + 1.

Extensions

a(8)-a(9) from Eric W. Weisstein, Jul 08 2013
Offset changed by Andrew Howroyd, Aug 11 2024

A225752 Positions of incrementally largest terms in the continued fraction of the Glaisher-Kinkelin constant A.

Original entry on oeis.org

0, 1, 4, 9, 12, 266, 3170, 3212, 12961, 82527
Offset: 1

Views

Author

Eric W. Weisstein, Jul 25 2013

Keywords

Comments

Correctly indexed version of A099792 using [a_0; a_1, a_2, ...].

Links

Crossrefs

Cf. A099792 (= a(n) + 1).
Cf. A099791 (incrementally largest terms).
Cf. A087501 (continued fraction).

Formula

a(n) = A099792(n) - 1.

Extensions

Offset changed by Andrew Howroyd, Aug 11 2024

A193547 Decimal expansion of 6*log(A) - 1/2 - 2*log(2)/3, where A is the Glaisher-Kinkelin constant (A074962).

Original entry on oeis.org

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

Views

Author

John M. Campbell, Jul 30 2011

Keywords

Examples

			0.530428...

Links

Crossrefs

Cf. A074962, A115521, A099791, A099792, A087501, A175820.

Programs

  • Mathematica
    N[-Integrate[(x (4 x^2 - x^4))/((-2 + x^2)^2 Log[1 - x^2]), {x, 0,  1}]]
RealDigits[-(1/2) - (2 Log[2])/3 + 6 Log[Glaisher], 10, 200]
  • PARI
    -6*zeta'(-1)-2*log(2)/3 \\ Charles R Greathouse IV, Dec 12 2013

Formula

Equals: -integral(x=0..1, x*(4*x^2 - x^4) / ((-2 + x^2)^2 * log(1 - x^2)) ). See Guillera & Sondow link for a related product.
Showing 1-3 of 3 results.

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