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A347430 Simple continued fraction expansion of Pi^(3/2)/Gamma(3/4)^2.

%I A347430 #24 Feb 16 2025 08:34:02
%S A347430 3,1,2,2,2,1,8,1,2,1,2,9,8,6,56,5,38,1,2,1,5,1,5,1,2,10,3,10,741,1,5,
%T A347430 3,3,1,5,2,3,1,1,1,1,2,1,1,2,2,1,7,2,3,3,4,4,1,11,1,2,1,1,1,1,1,5,1,
%U A347430 64,1,1,2,7,1,5,98,2,2,2,1,1,1,1,1,5,1,3,1
%N A347430 Simple continued fraction expansion of Pi^(3/2)/Gamma(3/4)^2.
%H A347430 M. Parker, <a href="https://www.youtube.com/watch?v=gjtTcyWL0NA">What is the area of a Squircle?</a>, Youtube video (2021).
%H A347430 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squircle.html">Squircle</a>
%F A347430 Equals sqrt(2)*Pi/agm(1,sqrt(2)) (arithmetic-geometric mean).
%F A347430 Equals 8*Gamma(5/4)^2/sqrt(Pi). - _Peter Luschny_, Sep 02 2021
%e A347430 3+1/(1+1/(2+1/(2+1/(2+...)))).
%p A347430 convert(8*GAMMA(5/4)^2/sqrt(Pi), confrac, 84); # _Peter Luschny_, Sep 02 2021
%t A347430 ContinuedFraction[Pi^(3/2)/Gamma[3/4]^2, 84] (* _Michael De Vlieger_, Sep 01 2021 *)
%o A347430 (PARI) contfrac(Pi^1.5/gamma(3/4)^2) \\ _Michel Marcus_, Sep 02 2021
%Y A347430 Cf. A175576 for decimal expansion.
%K A347430 nonn,cofr
%O A347430 0,1
%A A347430 _Adam Filinovich_, Sep 01 2021