A227718 Decimal expansion of the length of the quartic curve with implicit Cartesian equation x^4 + y^2 = 1 (sometimes called "elliptic lemniscate").

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

Offset

1,1

Links

Table of n, a(n) for n=1..100.

Serge Mehl, Lemniscate elliptique [in French].

Formula

4*Integral_{0..1} sqrt(1 + 4*x^6/(1 - x^4)).

Example

6.70715226023175940630529761383684415365444165289337602045878050700347311567787...

Mathematica

4*(NIntegrate[Sqrt[1 + (4*x^6)/(1 - x^4)], {x, 0, 3^(1/4)/Sqrt[2]}, WorkingPrecision -> 105] + NIntegrate[Sqrt[1 + (y/(2*(1 - y^2)^(3/4)))^2], {y, 0, 1/2}, WorkingPrecision -> 105]) // RealDigits[#, 10, 100]& // First

Crossrefs

Cf. A227717 (area).

Sequence in context: A011098 A344428 A224238 * A198932 A010499 A218012

Adjacent sequences: A227715 A227716 A227717 * A227719 A227720 A227721

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 22 2013

Status

approved