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A118178 Decimal expansion of arc length of eight curve. 0
6, 0, 9, 7, 2, 2, 3, 4, 7, 0, 1, 0, 4, 9, 1, 6, 0, 4, 6, 4, 3, 0, 3, 7, 4, 2, 0, 5, 6, 7, 3, 9, 9, 7, 8, 3, 3, 4, 9, 2, 3, 3, 7, 8, 1, 8, 3, 8, 6, 5, 5, 5, 1, 1, 4, 8, 6, 6, 1, 7, 3, 2, 1, 0, 0, 8, 2, 0, 4, 3, 7, 5, 4, 9, 4, 4, 1, 4, 0, 9, 3, 2, 0, 1, 3, 5, 4, 9, 6, 1, 4, 3, 3, 6, 5, 9, 1, 7, 6, 1, 0, 7, 7, 7, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Eight Curve

FORMULA

4*Integral_{t=0..Pi/2} (sqrt(4*sin(t)^4 - 5*sin(t)^2 + 2)) dt.

Can be expressed in terms of complete elliptic integrals. Using Mathematica notation, with m = (4 + Sqrt[2])/8, the arc length is 4*2^(1/4)*(EllipticE[m] - EllipticK[m]) + (3 + 2*Sqrt[2])*2^(-1/4)*EllipticPi[(4 - 3*Sqrt[2])/8, m]. - David W. Cantrell, Apr 22 2006

EXAMPLE

6.097223470104916046...

MATHEMATICA

RealDigits[4*NIntegrate[Sqrt[4*Sin[t]^4-5*Sin[t]^2+2], {t, 0, Pi/2}, WorkingPrecision->200], 10, 110][[1]]

CROSSREFS

Sequence in context: A189037 A153201 A248725 * A021168 A147709 A176403

Adjacent sequences:  A118175 A118176 A118177 * A118179 A118180 A118181

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Apr 13 2006

STATUS

approved

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Last modified September 23 03:40 EDT 2020. Contains 337291 sequences. (Running on oeis4.)