# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a064853 Showing 1-1 of 1 %I A064853 #39 Sep 24 2022 08:17:51 %S A064853 5,2,4,4,1,1,5,1,0,8,5,8,4,2,3,9,6,2,0,9,2,9,6,7,9,1,7,9,7,8,2,2,3,8, %T A064853 8,2,7,3,6,5,5,0,9,9,0,2,8,6,3,2,4,6,3,2,5,6,3,3,6,4,3,4,0,7,6,0,1,5, %U A064853 8,1,1,7,4,1,4,0,8,2,8,5,0,0,4,6,0,5,9,1,0,6,5,9,2,2,8,5,8,1,8,6,8,9 %N A064853 Lemniscate constant. %H A064853 Harry J. Smith, Table of n, a(n) for n = 1..5000 %H A064853 Markus Faulhuber, Anupam Gumber, and Irina Shafkulovska, The AGM of Gauss, Ramanujan's corresponding theory, and spectral bounds of self-adjoint operators, arXiv:2209.04202 [math.CA], 2022, p. 15. %H A064853 Eric Weisstein's World of Mathematics, Lemniscate Constant. %H A064853 Eric Weisstein's World of Mathematics, Lemniscate. %H A064853 Index entries for transcendental numbers. %F A064853 Equals Gamma(1/4)^2/sqrt(2*Pi). - _G. C. Greubel_, Oct 07 2018 %F A064853 Equals 2*A062539 = 4*A085565. - _Amiram Eldar_, May 04 2022 %F A064853 From _Stefano Spezia_, Sep 23 2022: (Start) %F A064853 Equals 4*Integral_{x=0..Pi/2} 1/sqrt(2*(1 - (1/2)*sin(x)^2)) dx [Gauss, 1799] (see Faulhuber et al.). %F A064853 Equals 2*sqrt(2)*A093341. (End) %e A064853 5.244115108584239620929679... %t A064853 First@RealDigits[ N[ Gamma[ 1/4 ]^2/Sqrt[ 2 Pi ], 102 ] ] %o A064853 (PARI) { allocatemem(932245000); default(realprecision, 5080); x=gamma(1/4)^2/sqrt(2*Pi); for (n=1, 5000, d=floor(x); x=(x-d)*10; write("b064853.txt", n, " ", d)); } \\ _Harry J. Smith_, Jun 20 2009 %o A064853 (PARI) gamma(1/2)*gamma(1/4)/gamma(3/4) \\ _Charles R Greathouse IV_, Oct 29 2021 %o A064853 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Gamma(1/4)^2/Sqrt(2*Pi(R)); // _G. C. Greubel_, Oct 07 2018 %Y A064853 Cf. A002193, A019727, A062539, A068466, A085565, A093341. %K A064853 nonn,cons,easy %O A064853 1,1 %A A064853 _Eric W. Weisstein_, Sep 22 2001 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE