This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A105419 #15 Jun 06 2025 08:05:11
%S A105419 7,6,4,0,3,9,5,5,7,8,0,5,5,4,2,4,0,3,5,8,0,9,5,2,4,1,6,4,3,4,2,8,8,6,
%T A105419 5,8,3,8,1,9,9,3,5,2,2,9,2,9,4,5,4,9,4,4,2,1,6,0,9,9,3,3,1,3,4,9,4,3,
%U A105419 9,1,6,0,2,4,2,8,6,5,9,8,4,2,1,3,2,3,6,2,1,7,8,9,0,2,4,4,4,9,6,5,6,4,4,0,8
%N A105419 Decimal expansion of the arc length of the sine or cosine curve for one full period.
%D A105419 Howard Anton, Irl C. Bivens, Stephen L. Davis, Calculus, Early Transcendentals, 7th Edition, John Wiley & Sons, Inc., NY, Section 7.4 Length of a Plane Curve, page 489.
%F A105419 Equals Integral_{x=0..2*Pi} sqrt(1+cos(x)^2) dx.
%F A105419 Also equals 4*B+Pi/B where B is the lemniscate constant A076390, or sqrt(2/Pi)*(2*gamma(3/4)^4 + Pi^2)/gamma(3/4)^2. - _Jean-François Alcover_, Apr 17 2013
%e A105419 I=7.640395578055424035809524164342886583819935229294549442160993313...
%p A105419 evalf(4*sqrt(2)*EllipticE(1/sqrt(2)), 120); # _Vaclav Kotesovec_, Apr 22 2015
%t A105419 RealDigits[ NIntegrate[ Sqrt[1 + Cos[x]^2], {x, 0, 2Pi}, MaxRecursion -> 12, WorkingPrecision -> 128], 10, 111][[1]]
%t A105419 RealDigits[ N[ 4*Sqrt[2]*EllipticE[1/2], 105]][[1]] (* _Jean-François Alcover_, Nov 08 2012 *)
%K A105419 cons,nonn
%O A105419 1,1
%A A105419 _Robert G. Wilson v_, Apr 06 2005