A087501 -id:A087501 - cp's OEIS frontend

A099791 Records for terms in the continued fraction of the Glaisher-Kinkelin constant A.

Original entry on oeis.org

1, 3, 5, 12, 271, 12574, 13740, 78907, 133430, 574536

Offset: 1

Eric W. Weisstein, Oct 27 2004

Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant

Cf. A087501, A225752.

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

Eric W. Weisstein, Jul 25 2013

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

Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant Continued Fraction

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

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

Offset changed by Andrew Howroyd, Aug 11 2024

A225762 Position of the first occurrence of n in continued fraction for the Glaisher-Kinkelin constant.

Original entry on oeis.org

0, 15, 1, 10, 4, 19, 16, 77, 21, 62, 229, 9, 52, 275, 30, 129, 200, 74, 240, 934, 1114, 401, 517, 33, 1433, 76, 431, 144, 742, 248, 521, 541, 3614, 1585, 18, 584, 691, 168, 35, 471, 352, 236, 869, 637, 258, 6100, 1459, 163, 1550, 1821, 1325, 1582, 885, 2751, 568

Offset: 1

Eric W. Weisstein, Jul 25 2013

Eric W. Weisstein, Table of n, a(n) for n = 1..203
Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant Continued Fraction

Cf. A087501 (continued fraction of the Glaisher-Kinkelin constant).

A279919 Numerators of convergents to Glaisher-Kinkelin constant (A074962).

Original entry on oeis.org

1, 4, 5, 9, 50, 59, 109, 168, 613, 7524, 30709, 38233, 10391852, 10430085, 20821937, 52073959, 385339650, 437413609, 15694815965, 94606309399, 110301125364, 1087316437675, 4459566876064, 10006450189803, 14466017065867, 24472467255670, 63410951577207, 87883418832877

Offset: 1

Ilya Gutkovskiy, Dec 23 2016

			1, 4/3, 5/4, 9/7, 50/39, 59/46, 109/85, 168/131, 613/478, 7524/5867, 30709/23946, 38233/29813, ...

Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant

Cf. A074962, A087501, A279920.

Mathematica
```
Numerator[Convergents[Glaisher, 28]]
```

A279920 Denominators of convergents to Glaisher-Kinkelin constant (A074962).

Original entry on oeis.org

1, 3, 4, 7, 39, 46, 85, 131, 478, 5867, 23946, 29813, 8103269, 8133082, 16236351, 40605784, 300476839, 341082623, 12238368644, 73771294487, 86009663131, 847858262666, 3477442713795, 7802743690256, 11280186404051, 19082930094307, 49446046592665, 68528976686972

Offset: 1

Ilya Gutkovskiy, Dec 23 2016

			1, 4/3, 5/4, 9/7, 50/39, 59/46, 109/85, 168/131, 613/478, 7524/5867, 30709/23946, 38233/29813, ...

Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant

Cf. A074962, A087501, A279919.

Mathematica
```
Denominator[Convergents[Glaisher, 28]]
```

A193547 Decimal expansion of 6log(A) - 1/2 - 2log(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

John M. Campbell, Jul 30 2011

			0.530428...

J. Guillera, J. Sondow, Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent, (2006), p. 16-17

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

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]

-6*zeta'(-1)-2*log(2)/3 \\ Charles R Greathouse IV, Dec 12 2013

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.

cp's OEIS Frontend

A099791 Records for terms in the continued fraction of the Glaisher-Kinkelin constant A.

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

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Extensions

A225762 Position of the first occurrence of n in continued fraction for the Glaisher-Kinkelin constant.

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A279919 Numerators of convergents to Glaisher-Kinkelin constant (A074962).

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Mathematica

A279920 Denominators of convergents to Glaisher-Kinkelin constant (A074962).

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Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

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

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Author

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Examples

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Crossrefs

Programs

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Formula

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