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Revision History for A016627

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A016627

Decimal expansion of log(4).
(history; published version)

#121 by Russ Cox at Sun Jan 05 19:51:34 EST 2025

LINKS

H.-J. Seiffert, <a href="https://fq.math.ca/Scanned/32-4/elementary32-4.pdf">Problem B-771</a>, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 32, No. 4 (1994), p. 374; <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/33-5/elementary33-5.pdf">More Sums</a>, Solution to Problem B-771 by Don Redmond, ibid., Vol. 33, No. 5 (1995), pp. 470-471.

Discussion

Sun Jan 05

19:51

OEIS Server: https://oeis.org/edit/global/3012

#120 by Michael De Vlieger at Fri Dec 27 18:25:40 EST 2024

STATUS

reviewed

approved

#119 by Hugo Pfoertner at Fri Dec 27 16:09:02 EST 2024

STATUS

proposed

reviewed

#118 by Stefano Spezia at Fri Dec 27 15:24:32 EST 2024

STATUS

editing

proposed

#117 by Stefano Spezia at Fri Dec 27 13:06:25 EST 2024

LINKS

Lawrence Downey, Boon W. Ong , and James A. Sellers, <a href="https://www.d.umn.edu/~jsellers/downey_ong_sellers_cmj_preprint.pdf">Beyond the Basel Problem: Sums of Reciprocals of Figurate Numbers</a>, Coll. Math. J., 39, no. 5 (2008), 391-394.

Allon G. Percus, Gabriel Istrate, Bruno Goncalves, Robert Z. Sumi , and Stefan Boettcher, <a href="http://arxiv.org/abs/0808.1549">The Peculiar Phase Structure of Random Graph Bisection</a>, arXiv:0808.1549 [cond-mat.stat-mech], 2008.

#116 by Stefano Spezia at Fri Dec 27 12:31:28 EST 2024

REFERENCES

Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 2, equation 2:13:8 at page 23.

FORMULA

Equals Sum_{n>=1} (2*n - 1)!!/(n*(2*n)!!) [Ross] (see Spanier at p. 23). - Stefano Spezia, Dec 27 2024

STATUS

approved

editing

#115 by Hugo Pfoertner at Thu Mar 21 07:03:31 EDT 2024

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proposed

approved

#114 by Vaclav Kotesovec at Thu Mar 21 07:01:45 EDT 2024

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editing

proposed

#113 by Vaclav Kotesovec at Thu Mar 21 07:01:31 EDT 2024

FORMULA

log(4) = 2*Sum_{n >= 1} 1/(n*P(n, 5/3)*P(n-1, 5/3)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(54) = 1.386294361119890618(66...), correct to 18 decimal places. - Peter Bala, Mar 18 2024

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reviewed

editing

#112 by Joerg Arndt at Thu Mar 21 05:52:46 EDT 2024

STATUS

proposed

reviewed