Search: id:A118178
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%I A118178
%S A118178 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,
%T A118178 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,
%U A118178 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
%N A118178 Decimal expansion of arc length of eight curve.
%H A118178 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EightCurve.html">Eight Curve</a>
%F A118178 4*Integrate[Sqrt[4*Sin[t]^4-5*Sin[t]^2+2], {t, 0, Pi/2}].
%F A118178 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
%e A118178 6.097223470104916046...
%t A118178 RealDigits[4*NIntegrate[Sqrt[4*Sin[t]^4-5*Sin[t]^2+2],{t,0,Pi/2},WorkingPrecision->
               200],10,110][[1]]
%Y A118178 Sequence in context: A016628 A112246 A153201 this_sequence A021168 A147709 
               A153314
%Y A118178 Adjacent sequences: A118175 A118176 A118177 this_sequence A118179 A118180 
               A118181
%K A118178 nonn,cons
%O A118178 1,1
%A A118178 Eric Weisstein (eric(AT)weisstein.com), Apr 13, 2006

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