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%I #31 Jun 24 2021 07:32:56
%S 4,7,4,9,4,9,3,7,9,9,8,7,9,2,0,6,5,0,3,3,2,5,0,4,6,3,6,3,2,7,9,8,2,9,
%T 6,8,5,5,9,5,4,9,3,7,3,2,1,7,2,0,2,9,8,2,2,8,3,3,3,1,0,2,4,8,6,4,5,5,
%U 7,9,2,9,1,7,4,8,8,3,8,6,0,2,7,4,2,7,5,6,4,1,2,5,0,5,0,2,1,4,4,4,1,8,9,0,3
%N Decimal expansion of 2^(5/4)*sqrt(Pi)*exp(Pi/8)/Gamma(1/4)^2.
%C Decimal expansion of sigma(1|1,i)/2, where sigma is the Weierstrass sigma function and 1 and i are the half-periods. - _Eric W. Weisstein_, Jan 15 2005
%C Known to be transcendental. - _Benoit Cloitre_, Jan 07 2006
%C Called "Weierstrass constant" after the German mathematician Karl Theodor Wilhelm Weierstrass (1815-1897). - _Amiram Eldar_, Jun 24 2021
%D Michel Waldschmidt, Elliptic functions and transcendance, Surveys in number theory, 143-188, Dev. Math., 17, Springer, New York, 2008.
%H G. C. Greubel, <a href="/A094692/b094692.txt">Table of n, a(n) for n = 0..5000</a>
%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap93.html">2**(5/4)*sqrt(Pi)*exp(Pi/8)*GAMMA(1/4)**(-2)</a>.
%H Michel Waldschmidt, <a href="http://people.math.jussieu.fr/~miw/articles/pdf/SurveyTrdceEllipt2006.pdf">Elliptic Functions and Transcendence</a>, preprint, Corollary 49.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WeierstrassConstant.html">Weierstrass Constant</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F c = 2^(5/4)*Pi^(1/2)*exp(Pi/8)/Gamma(1/4)^2.
%e 0.474949379987920650332...
%t RealDigits[2^(5/4) Sqrt[Pi] E^(Pi/8)/Gamma[1/4]^2, 10, 111][[1]]
%t RealDigits[N[WeierstrassSigma[1, WeierstrassInvariants[{1, I}]]/2, 100], 10][[1]] (* _Eric W. Weisstein_, Apr 16 2018 *)
%o (PARI) 2^(5/4)*Pi^(1/2)*exp(Pi/8)/gamma(1/4)^2 \\ _Benoit Cloitre_, Jan 07 2006
%K cons,nonn
%O 0,1
%A _Robert G. Wilson v_, May 19 2004
%E Edited by _N. J. A. Sloane_, Aug 19 2008 at the suggestion of _R. J. Mathar_
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