A227717 Decimal expansion of the area of the quartic curve with implicit Cartesian equation x^4 + y^2 = 1 (sometimes called "elliptic lemniscate").

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

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-François Alcover, Jul 22 2013

Status

approved