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 A327996 #20 May 30 2023 11:25:45 %S A327996 9,6,2,8,2,7,7,8,2,4,4,6,4,1,7,5,4,7,9,1,9,0,9,2,2,1,5,4,4,8,5,2,2,9, %T A327996 7,8,2,7,1,0,0,8,5,1,4,4,7,8,5,8,0,6,7,1,0,0,1,8,2,1,5,1,4,9,5,0,0,4, %U A327996 5,5,3,5,7,5,7,5,5,0,9,8,6,9,7,0,9,1 %N A327996 Decimal expansion of (1/2)*Pi^(3/4)/Gamma(3/4). %C A327996 The function df(x) = 2^(x/2)*(2/Pi)^(sin(Pi*x/2)^2/2)*Gamma(x/2+1) interpolates the double factorials A006882 and extends them analytically. df(1/2) is the given constant. Extending also the notation this can be written as (1/2)!! = Pi^(3/4)/(2*(-1/4)!). %F A327996 Equals Pi^(3/4)/(2*(-1/4)!). %F A327996 From _Amiram Eldar_, May 30 2023: (Start) %F A327996 Equals Gamma(1/4)/(2*sqrt(2)*Pi^(1/4)). %F A327996 Equals A319332 * sqrt(Pi). (End) %e A327996 Equals 0.962827782446417547919092215448522978271008514478580671... %p A327996 Digits := 100: (1/2)*Pi^(3/4)/GAMMA(3/4)*10^86: %p A327996 ListTools:-Reverse(convert(floor(%), base, 10)); %t A327996 RealDigits[Pi^(3/4)/(2*Gamma[3/4]), 10, 120][[1]] (* _Amiram Eldar_, May 30 2023 *) %o A327996 (PARI) (1/2)*Pi^(3/4)/gamma(3/4) \\ _Michel Marcus_, Oct 24 2019 %Y A327996 Cf. A006882, A319332, A327995. %K A327996 nonn,cons %O A327996 0,1 %A A327996 _Peter Luschny_, Oct 24 2019