cp's OEIS Frontend

A118322 Decimal expansion of perimeter of the closed portion of the bow curve.

%I A118322 #16 Apr 07 2025 10:06:39
%S A118322 1,9,2,1,5,1,1,3,6,5,1,7,2,5,1,2,5,7,0,1,5,6,2,9,9,8,2,6,0,5,9,7,4,0,
%T A118322 8,3,6,5,7,6,1,3,0,4,9,0,5,2,7,6,2,4,2,5,5,4,5,4,4,1,5,7,6,4,8,3,1,8,
%U A118322 9,3,1,0,5,4,6,3,2,7,7,9,6,1,4,7,0,5,8,3,9,5,1,8,6,4,2,9,0,2,0,5,5,2,6,0,4
%N A118322 Decimal expansion of perimeter of the closed portion of the bow curve.
%C A118322 Writing x=r*cos(phi), y=r*sin(phi), r=sin(phi)*(1-2*sin^2(phi))/cos^4(phi) in circular coordinates gives the arc length of one wing of Integral_{phi=0..Pi/4} sqrt((dx/dphi)^2 + (dy/dphi)^2) dphi = Integral_{s=0..1/sqrt(2)} sqrt(1-5*s^2+20*s^6) / (1-s^2)^3 ds. - _R. J. Mathar_, Mar 23 2010
%H A118322 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Bow.html">Bow</a>
%e A118322 1.9215113651725125701...
%p A118322 Digits := 120 : f := 2*sqrt(1-5*x^2+20*x^6)/(1-x^2)^3 ; Int(f,x=0..1/sqrt(2.0)) ; x := evalf(%) ; # _R. J. Mathar_, Mar 23 2010
%t A118322 f[x_] := 2*Sqrt[1-5*x^2+20*x^6]/(1-x^2)^3; First[ RealDigits[ NIntegrate[f[x], {x, 0, 1/Sqrt[2]}, WorkingPrecision -> 120], 10, 105]](* _Jean-François Alcover_, Jun 08 2012, after _R. J. Mathar_ *)
%K A118322 nonn,cons
%O A118322 1,2
%A A118322 _Eric W. Weisstein_, Apr 23 2006
%E A118322 More digits from _R. J. Mathar_, Mar 23 2010