The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A249282

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A249282

Decimal expansion of K(1/4), where K is the complete elliptic integral of the first kind.
(history; published version)

#18 by N. J. A. Sloane at Mon Mar 25 21:35:17 EDT 2024

STATUS

proposed

approved

#17 by Michel Marcus at Mon Mar 25 18:04:44 EDT 2024

STATUS

editing

proposed

#16 by Michel Marcus at Mon Mar 25 18:04:41 EDT 2024

LINKS

Eric Weisstein's MathWorld, World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteEllipticIntegraloftheFirstKind.html">Complete Elliptic Integral of the First Kind</a>

STATUS

proposed

editing

#15 by Paul D. Hanna at Mon Mar 25 14:17:52 EDT 2024

STATUS

editing

proposed

#14 by Paul D. Hanna at Mon Mar 25 14:17:34 EDT 2024

FORMULA

K(1/4) = Pi/2 * sqrt( Sum_{n>=0} binomial(2*n,n)^3/16^n * (m*(1/4)*(3/4-m))^n ), where m = 1/4. (End)

#13 by Paul D. Hanna at Mon Mar 25 14:09:05 EDT 2024

FORMULA

From Paul D. Hanna, Mar 25 2024: (Start)

K(1/4) = Pi/2 * Sum_{n>=0} binomial(2*n,n)^2/16^n * (1/4)^n.

K(1/4) = Pi/2 * sqrt( Sum_{n>=0} binomial(2*n,n)^3/16^n * ((1/4)*(3/4))^n ). (End)

STATUS

approved

editing

#12 by Joerg Arndt at Sat Jun 03 09:57:22 EDT 2017

STATUS

proposed

approved

#11 by Antti Karttunen at Sat Jun 03 09:57:03 EDT 2017

STATUS

editing

proposed

#10 by Antti Karttunen at Sat Jun 03 09:55:03 EDT 2017

LINKS

Steven Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/csolve/ge.pdf">Gergonne-Schwarz Surface</a>

Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/CompleteEllipticIntegraloftheFirstKind.html">Complete Elliptic Integral of the First Kind</a>

#9 by Antti Karttunen at Sat Jun 03 09:54:24 EDT 2017

LINKS

Steven R. Finch, <a href="/A249282/a249282.pdf">Gergonne-Schwarz Surface</a>, April 12, 2013. [Cached copy, with permission of the author]

STATUS

approved

editing