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 A363848 #43 Jul 31 2023 16:56:26
%S A363848 9,3,3,1,7,4,6,5,3,4,9,8,4,6,2,6,4,4,0,1,5,5,4,4,5,3,5,2,4,8,4,6,1,0,
%T A363848 6,1,0,8,6,7,7,3,8,5,6,2,0,1,9,3,4,9,4,3,5,9,0,1,0,3,7,9,9,8,2,3,6,3,
%U A363848 0,9,4,1,8,6,5,4,2,6,2,0,3,4,4,7,5,1,9,6
%N A363848 Decimal expansion of the arithmetic mean of the isoperimetric quotient of ellipses when expressed in terms of their eccentricity.
%C A363848 The isoperimetric quotient of a curve is defined as Q = (4*Pi*A)/p^2, where A and p are the area and the perimeter of that curve respectively.
%C A363848 The isoperimetric quotient of an ellipse depends only on its eccentricity e in accordance to the formula Q = (Pi^2*sqrt(1-e^2))/(4*E(e)^2), where E() is the complete elliptic integral of the second kind.
%H A363848 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IsoperimetricQuotient.html">Isoperimetric Quotient</a>
%H A363848 Wikipedia, <a href="https://en.m.wikipedia.org/wiki/Elliptic_integral">Elliptic integral</a>
%F A363848 Equals ((Pi^2)/4) * Integral_{x=0..1} sqrt(1 - x^2)/E(x)^2 dx.
%e A363848 0.933174653498462644...
%t A363848 First[RealDigits[Pi^2/4 * NIntegrate[Sqrt[1-x^2]/EllipticE[x^2]^2, {x,0,1}, WorkingPrecision -> 100]]] (* _Stefano Spezia_, Jun 24 2023 *)
%Y A363848 Cf. A091476, A363874, A363876.
%K A363848 nonn,cons
%O A363848 0,1
%A A363848 _Tian Vlasic_, Jun 24 2023
%E A363848 More terms from _Stefano Spezia_, Jun 24 2023