The On-Line Encyclopedia of Integer Sequences (OEIS)

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A103711

Decimal expansion of the ratio of the length of the latus rectum arc of any parabola to its latus rectum: (sqrt(2) + log(1 + sqrt(2)))/2.
(history; published version)

#90 by Charles R Greathouse IV at Sun Feb 16 08:32:56 EST 2025

LINKS

S. Reese and Jonathan Sondow, <a href="httphttps://mathworld.wolfram.com/UniversalParabolicConstant.html">Universal Parabolic Constant</a>, MathWorld

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/UniversalParabolicConstant.html">Universal Parabolic Constant</a>

Discussion

Sun Feb 16

08:32

OEIS Server: https://oeis.org/edit/global/3014

#89 by Alois P. Heinz at Tue Dec 17 16:46:00 EST 2024

STATUS

proposed

approved

#88 by Antonio Graciá Llorente at Tue Dec 17 16:14:49 EST 2024

STATUS

editing

proposed

#87 by Antonio Graciá Llorente at Tue Dec 17 16:14:46 EST 2024

FORMULA

Equals Sum_{n>=0} (-1)^(n + 1)*Binomialbinomial(2*n, n)/((4*n^2 - 1)*4^n). - Antonio Graciá Llorente, Dec 16 2024

#86 by Alois P. Heinz at Tue Dec 17 11:48:54 EST 2024

STATUS

proposed

editing

Discussion

Tue Dec 17

11:50

Alois P. Heinz: binomial(n,k) or C(n,k) for binomial coefficients; the former is preferred but the latter is acceptable in formulas if there are quite a few coefficients. Capitalize "Binomial" only at the beginning of sentence
from: https://oeis.org/wiki/Style_Sheet#Spelling_and_notation

#85 by Michel Marcus at Tue Dec 17 00:56:26 EST 2024

STATUS

editing

proposed

#84 by Michel Marcus at Tue Dec 17 00:55:54 EST 2024

LINKS

S. Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Mathematical Constants, Errata and Addenda</a>, arXiv:2001.00578 [math.HO], 2012, -2024, section 8.1.

S. Reese, J. and Jonathan Sondow, <a href="http://mathworld.wolfram.com/UniversalParabolicConstant.html">Universal Parabolic Constant</a>, MathWorld

J. Jonathan Sondow, <a href="http://arxiv.org/abs/1210.2279">The parbelos, a parabolic analog of the arbelos</a>, arXiv 2012, Amer. Math. Monthly, 120 (2013), 929-935.

STATUS

proposed

editing

#83 by Antonio Graciá Llorente at Mon Dec 16 18:25:10 EST 2024

STATUS

editing

proposed

#82 by Antonio Graciá Llorente at Mon Dec 16 18:25:07 EST 2024

FORMULA

Equals Sum_{n>=0} (-1)^(n + 1)*Binomial(2*n, n)/((4*n^2 - 1)*4^n). - Antonio Graciá Llorente, Dec 16 2024

STATUS

approved

editing

#81 by Charles R Greathouse IV at Sat Oct 19 15:57:32 EDT 2024

LINKS

H. Khelif, <a href="http://images-archive.math.cnrs.fr/L-arbelos-Partie-II.html#nb4">L’arbelos, Partie II, Généralisations de l’arbelos</a>, Images des Mathématiques, CNRS, 2014.

Discussion

Sat Oct 19

15:57

OEIS Server: https://oeis.org/edit/global/3000