A154743 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.

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

Offset

0,1

Comments

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

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Index entries for algebraic numbers, degree 4

Example

0.348310699749006523686374494327...

Mathematica

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

Prog

(PARI) sqrtn(2, 4) - sqrtn(2, -4) \\ Michel Marcus, Dec 10 2016
(PARI) polrootsreal(2*x^4+8*x^2-1)[2] \\ Charles R Greathouse IV, Nov 07 2017
(Magma) [2^(1/4) - 2^(-1/4)]; // G. C. Greubel, Nov 05 2017

Crossrefs

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

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

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

Sequence in context: A088745 A213922 A306568 * A020812 A021291 A179104

Adjacent sequences: A154740 A154741 A154742 * A154744 A154745 A154746

Keyword

nonn,cons,easy

Author

Stuart Clary, Jan 14 2009

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009

Status

approved