OFFSET
0,1
COMMENTS
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)!).
FORMULA
Equals Pi^(3/4)/(2*(-1/4)!).
From Amiram Eldar, May 30 2023: (Start)
Equals Gamma(1/4)/(2*sqrt(2)*Pi^(1/4)).
Equals A319332 * sqrt(Pi). (End)
EXAMPLE
Equals 0.962827782446417547919092215448522978271008514478580671...
MAPLE
Digits := 100: (1/2)*Pi^(3/4)/GAMMA(3/4)*10^86:
ListTools:-Reverse(convert(floor(%), base, 10));
MATHEMATICA
RealDigits[Pi^(3/4)/(2*Gamma[3/4]), 10, 120][[1]] (* Amiram Eldar, May 30 2023 *)
PROG
(PARI) (1/2)*Pi^(3/4)/gamma(3/4) \\ Michel Marcus, Oct 24 2019
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Peter Luschny, Oct 24 2019
STATUS
approved