Search: id:A154739
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%I A154739
%S A154739 5,4,1,1,9,6,1,0,0,1,4,6,1,9,6,9,8,4,3,9,9,7,2,3,2,0,5,3,6,6,
%T A154739 3,8,9,4,2,0,0,6,1,0,7,2,0,6,3,3,7,8,0,1,5,4,4,4,6,8,1,2,9,7,
%U A154739 0,9,5,6,5,2,9,8,8,9,7,3,5,4,1,0,1,2,6,6,6,4,7,7,8,2,6,1,4,9,5
%N A154739 Decimal expansion of sqrt{1 - 1/sqrt{2}}, the abscissa of the point of 
               bisection of the arc of the unit lemniscate (x^2 + y^2)^2 = x^2 - 
               y^2 in the first quadrant.
%D A154739 C. L. Siegel, Topics in Complex Function Theory, Volume I: Elliptic Functions 
               and Uniformization Theory, Wiley-Interscience, 1969, page 5
%e A154739 sqrt{1 - 1/sqrt{2}} = 0.541196100146196984399723205366..., a root of 
               2 x^4 - 4 x^2 + 1 = 0.
%t A154739 nmax = 1000; First[ RealDigits[ Sqrt[ 1 - 1/Sqrt[2] ], 10, nmax] ]
%Y A154739 Cf. A154743 for the ordinate and A154747 for the radius vector.
%Y A154739 Cf. A154740, A154741 and A154742 for the continued fraction and the numerators 
               and denominators of the convergents.
%Y A154739 Cf. A085565 for 1.311028777, the first-quadrant arc length of the unit 
               lemniscate.
%Y A154739 Sequence in context: A124602 A132707 A046575 this_sequence A136564 A136042 
               A166044
%Y A154739 Adjacent sequences: A154736 A154737 A154738 this_sequence A154740 A154741 
               A154742
%K A154739 nonn,cons,easy
%O A154739 0,1
%A A154739 Stuart Clary (clary(AT)uakron.edu), Jan 14, 2009
%E A154739 Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 
               05 2009

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