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

Author

Stuart Clary, Jan 14 2009

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			0.348310699749006523686374494327...
		

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

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.

Programs

Magma

[2^(1/4) - 2^(-1/4)]; // G. C. Greubel, Nov 05 2017

Mathematica

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

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

Extensions

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