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A227718 Decimal expansion of the length of the quartic curve with implicit Cartesian equation x^4 + y^2 = 1 (sometimes called "elliptic lemniscate"). 1
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified May 18 23:43 EDT 2024. Contains 372666 sequences. (Running on oeis4.)