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 A276627 #27 Feb 05 2025 00:09:35 %S A276627 1,5,8,2,5,5,1,7,2,7,2,2,3,7,1,5,9,1,1,8,3,3,1,3,5,0,7,1,0,7,0,4,0,9, %T A276627 8,7,6,5,2,9,4,8,8,1,4,9,6,1,8,7,8,9,2,4,3,4,9,7,1,6,9,4,4,8,4,7,8,2, %U A276627 0,8,5,3,5,1,8,6,6,6,3,5,5,1,7,3,6,2,0,9,8,1,4,0,6,5,5,4,3,2,2,2,0,0,0,4,1 %N A276627 Decimal expansion of K(3-2*sqrt(2)), where K is the complete elliptic integral of the first kind. %C A276627 The modulus k=3-2*sqrt(2). %C A276627 K(k_4) in the MathWorld link. %H A276627 G. C. Greubel, <a href="/A276627/b276627.txt">Table of n, a(n) for n = 1..10000</a> %H A276627 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EllipticIntegralSingularValue.html">Elliptic Integral Singular Values</a> %H A276627 I. J. Zucker and G. S. Joyce, <a href="https://doi.org/10.1017/S0305004101005254">Special values of the hypergeometric series II</a>, Math. Proc. Camb. Phil. Soc. 131 (2001) 309-319. Table 1 N=4. %F A276627 Equals 2*(2+sqrt(2))*Pi^(3/2)/Gamma(-1/4)^2. %F A276627 Equals A174968 * A062539 / 2. - _R. J. Mathar_, Aug 18 2023 %F A276627 Equals A093341 * A201488 [Zucker]. - _R. J. Mathar_, Jun 24 2024 %e A276627 1.58255172722371591183313507107040987652948814961878924349716944847... %p A276627 evalf(2*(2+sqrt(2))*Pi^(3/2)/GAMMA(-1/4)^2,120); # _Muniru A Asiru_, Oct 08 2018 %t A276627 RealDigits[N[EllipticK[(3 - 2 Sqrt[2])^2], 105]][[1]] %t A276627 RealDigits[2*(2+Sqrt[2])*Pi^(3/2)/Gamma[-1/4]^2, 10, 100][[1]] (* _G. C. Greubel_, Oct 08 2018 *) %o A276627 (PARI) default(realprecision, 100); 2*(2+sqrt(2))*Pi^(3/2)/gamma(-1/4)^2 \\ _G. C. Greubel_, Oct 08 2018 %o A276627 (PARI) ellK(3-sqrt(8)) \\ _Charles R Greathouse IV_, Feb 05 2025 %o A276627 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 2*(2+Sqrt(2))*Pi(R)^(3/2)/Gamma(-1/4)^2; // _G. C. Greubel_, Oct 08 2018 %Y A276627 Cf. A157259 (for 3-2*sqrt(2)). %K A276627 nonn,cons %O A276627 1,2 %A A276627 _Benedict W. J. Irwin_, Sep 07 2016