A154743 - OEIS

%I #18 Aug 21 2023 12:15:17

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

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

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

%N Decimal expansion of 2^(1/4) - 2^(-1/4), the ordinate 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.

%C A quartic integer with denominator 2: the positive root of 2x^4 + 8x^2 - 1 = 0.

%D C. L. Siegel, Topics in Complex Function Theory, Volume I: Elliptic Functions and Uniformization Theory, Wiley-Interscience, 1969, page 5

%H G. C. Greubel, <a href="/A154743/b154743.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>

%e 0.348310699749006523686374494327...

%t nmax = 1000; First[ RealDigits[ 2^(1/4) - 2^(-1/4), 10, nmax] ]

%o (PARI) sqrtn(2, 4) - sqrtn(2, -4) \\ _Michel Marcus_, Dec 10 2016

%o (PARI) polrootsreal(2*x^4+8*x^2-1)[2] \\ _Charles R Greathouse IV_, Nov 07 2017

%o (Magma) [2^(1/4) - 2^(-1/4)]; // _G. C. Greubel_, Nov 05 2017

%Y Cf. A154739 for the abscissa and A154747 for the radius vector.

%Y Cf. A154744, A154745 and A154746 for the continued fraction and the numerators and denominators of the convergents.

%Y Cf. A085565 for 1.311028777..., the first-quadrant arc length of the unit lemniscate.

%K nonn,cons,easy

%O 0,1

%A _Stuart Clary_, Jan 14 2009

%E Offset corrected by _R. J. Mathar_, Feb 05 2009