|
%I #22 Sep 08 2022 08:45:03
%S 2,1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1,10,2,4,1,8,2,1,5,3,11,3,
%T 17,2,338,2,3,1,1,6,3,1,2,1,1,1,2,1,2,3,9,1,1,1,2,21,1,1,2,5,3,1,1,3,
%U 1,1,10,1,1,1,40,1,2,7,1,1,2,2,2,1,1,2,81,1,2,2,1,1,4,8,3,5,1,1,3,180,2,1
%N Continued fraction for the Lemniscate constant or Gauss's constant.
%H Harry J. Smith, <a href="/A062540/b062540.txt">Table of n, a(n) for n = 1..5000</a>
%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/lemni.txt">Lemniscate or Gauss constant</a>
%e 2.622057554292119810464839589891119413682754951431623162816821703...
%e 2.622057554292119810464839589... = 2 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 20 2009
%t ContinuedFraction[Sqrt[2*Pi^3]/(2*Gamma[3/4]^2), 100] (* _G. C. Greubel_, Oct 07 2018 *)
%o (PARI) contfrac(1/2*Pi^(3/2)/gamma(3/4)^2*2^(1/2))
%o (PARI) { allocatemem(932245000); default(realprecision, 5200); x=contfrac(Pi^(3/2)*sqrt(2)/(2*gamma(3/4)^2)); for (n=1, 5000, write("b062540.txt", n, " ", x[n])); } \\ _Harry J. Smith_, Jun 20 2009
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); ContinuedFraction(Sqrt(2*Pi(R)^3)/(2*Gamma(3/4)^2)); // _G. C. Greubel_, Oct 07 2018
%Y Cf. A062539.
%K easy,nonn,cofr
%O 1,1
%A _Jason Earls_, Jun 25 2001
|
