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A227717 Decimal expansion of the area of the quartic curve with implicit Cartesian equation x^4 + y^2 = 1 (sometimes called "elliptic lemniscate"). 2
3, 4, 9, 6, 0, 7, 6, 7, 3, 9, 0, 5, 6, 1, 5, 9, 7, 4, 7, 2, 8, 6, 4, 5, 2, 7, 8, 6, 5, 2, 1, 4, 9, 2, 5, 5, 1, 5, 7, 7, 0, 0, 6, 6, 0, 1, 9, 0, 8, 8, 3, 0, 8, 8, 3, 7, 5, 5, 7, 6, 2, 2, 7, 1, 7, 3, 4, 3, 8, 7, 4, 4, 9, 4, 2, 7, 2, 1, 9, 0, 0, 0, 3, 0, 7, 0, 6, 0, 7, 1, 0, 6, 1, 5, 2, 3, 8, 7, 9, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

Serge Mehl, Lemniscate elliptique [in French].

FORMULA

Equals 4*Integral_{0..1} sqrt(1 - x^4).

Equals sqrt(Pi)*Gamma(1/4)/(2*Gamma(7/4)).

Equals 1/3*sqrt(2/Pi)*Gamma(1/4)^2. - Vaclav Kotesovec, Jul 26 2013

EXAMPLE

3.4960767390561597472864527865214925515770066019088308837557622717343874494272...

MATHEMATICA

Sqrt[Pi]*Gamma[1/4]/(2*Gamma[7/4]) // RealDigits[#, 10, 100]& // First

PROG

(PARI) sqrt(2/Pi)*gamma(1/4)^2/3 \\ Michel Marcus, Jul 04 2015

CROSSREFS

Cf. A227718 (length).

Sequence in context: A140439 A023183 A102320 * A021290 A016656 A319021

Adjacent sequences:  A227714 A227715 A227716 * A227718 A227719 A227720

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jul 22 2013

STATUS

approved

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Last modified April 24 22:26 EDT 2019. Contains 322446 sequences. (Running on oeis4.)