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A064582 Real half-period for the Weierstrass elliptic function with invariants g2=0, g3=1. 3

%I

%S 1,5,2,9,9,5,4,0,3,7,0,5,7,1,9,2,8,7,4,9,1,3,1,9,4,1,7,2,3,0,8,8,2,4,

%T 3,5,8,5,7,2,8,2,8,9,4,7,1,6,0,9,2,9,4,9,6,0,6,1,8,1,1,6,8,5,9,0,9,5,

%U 2,2,3,6,1,7,9,9,3,7,4,2,7,6,4,6,8,8,3,8,5,2,0,5,6,5,8,7,5,3,4,4,6,5

%N Real half-period for the Weierstrass elliptic function with invariants g2=0, g3=1.

%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 652.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.1.1 Weierstrass Pe Function, p. 422.

%H G. C. Greubel, <a href="/A064582/b064582.txt">Table of n, a(n) for n = 1..5000</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 652.

%H Amrik Singh Nimbran, <a href="https://doi.org/10.13140/RG.2.2.32148.32643">Infinite series for omega-2 constant</a>, 2020.

%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/w2.txt">Link to Simon Plouffe's Inverter.</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Omega-2Constant.html">Omega-2 Constant.</a>

%F Equals Gamma(1/3)^3/(4*Pi).

%F Also equals 2*2^(1/3)*EllipticK(4*sqrt(3)-7)/(135+78*sqrt(3))^(1/6). - _Jean-Fran├žois Alcover_, Jun 18 2014

%e 1.5299540370571928749131941723...

%p s:= convert(evalf(GAMMA(1/3)^3/(4*Pi)/10, 140), string):

%p seq(parse(s[i+1]), i=1..104); # _Alois P. Heinz_, Jun 18 2014

%t First@RealDigits[ Chop[ First@N[ WeierstrassHalfPeriods[ {0, 1} ], 102 ] ] ]

%t RealDigits[Gamma[1/3]^3/(4 Pi), 10, 100][[1]] (* _Jan Mangaldan_, Jan 06 2017 *)

%o (PARI) gamma(1/3)^3/4/Pi \\ _Charles R Greathouse IV_, Apr 18 2016

%o (MAGMA) C<i> := ComplexField(); [Gamma(1/3)^3/(4*Pi(C))]; // _G. C. Greubel_, Nov 05 2017

%K nonn,easy,cons

%O 1,2

%A _Eric W. Weisstein_, Sep 22 2001

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Last modified March 2 12:06 EST 2021. Contains 341750 sequences. (Running on oeis4.)