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 A379664 #11 Feb 05 2025 00:18:19 %S A379664 7,4,5,7,4,9,1,8,7,3,1,6,3,2,9,6,0,9,9,6,2,4,8,2,0,6,5,3,5,3,4,5,1,1, %T A379664 0,4,3,0,2,6,7,5,1,9,7,9,8,3,2,2,1,8,6,7,2,3,3,7,4,1,3,3,7,1,0,7,0,1, %U A379664 0,2,5,2,0,7,5,3,5,9,1,5,2,3,2,8,6,2,9,8,9,8,4,8,2,2,2,8,2,5,4,1 %N A379664 Decimal expansion of hypergeom([1/2, 1/2], [1], -2). %D A379664 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 17, page 143. %F A379664 Equals hypergeom([1/2, 1/2], [1], 2/3)/sqrt(3). %F A379664 Equals 2*EllipticK(2/3)/(Pi*sqrt(3)). %e A379664 0.74574918731632960996248206535345110430267519798... %t A379664 RealDigits[Hypergeometric2F1[1/2,1/2,1,-2],10,100][[1]] (* or *) %t A379664 RealDigits[Hypergeometric2F1[1/2,1/2,1,2/3]/Sqrt[3],10,100][[1]] (* or *) %t A379664 RealDigits[2EllipticK[2/3]/(Pi Sqrt[3]),10,100][[1]] %o A379664 (PARI) hypergeom([1/2,1/2],1,2/3)/sqrt(3) \\ _Hugo Pfoertner_, Dec 29 2024 %o A379664 (PARI) hypergeom([1,1]/2,1,-2) \\ _Charles R Greathouse IV_, Feb 05 2025 %o A379664 (PARI) 2*ellK(sqrt(2/3))/Pi/sqrt(3) \\ _Charles R Greathouse IV_, Feb 05 2025 %Y A379664 Cf. A000796, A002194, A304656. %K A379664 nonn,cons %O A379664 0,1 %A A379664 _Stefano Spezia_, Dec 29 2024