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Search: id:A154743
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| A154743 |
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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. |
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6
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| 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
(list; cons; graph; listen)
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OFFSET
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0,1
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REFERENCES
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C. L. Siegel, Topics in Complex Function Theory, Volume I: Elliptic Functions and Uniformization Theory, Wiley-Interscience, 1969, page 5
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EXAMPLE
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2^{1/4} - 2^{-1/4} = 0.348310699749006523686374494327..., a root of 2 y^4 + 8 y^2 - 1 = 0.
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MATHEMATICA
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nmax = 1000; First[ RealDigits[ 2^(1/4) - 2^(-1/4), 10, nmax] ]
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CROSSREFS
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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: A100231 A016609 A088745 this_sequence A020812 A021291 A127122
Adjacent sequences: A154740 A154741 A154742 this_sequence A154744 A154745 A154746
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KEYWORD
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nonn,cons,easy
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AUTHOR
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Stuart Clary (clary(AT)uakron.edu), Jan 14, 2009
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EXTENSIONS
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Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009
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