The double factorial x!! yields an incorrect result for
x other than an integer. It appears that x!! is
computed as the product x*(x-2)*(x-4)*...*y, where y is
the least term (x-2*k) s.t. x-2*k > 1. This agrees with
published defns (Arfken, Mathworld) for positive
integers but not otherwise.
states a formula for z!!, z complex, translated into
Maxima as follows --
doublefact (z) := block ([a: 1+2*z-cos(%pi*z), b:
cos(%pi*z)-1], 2^(a/4) * %pi^(b/4) * gamma(1+z/2));
It seems that Maxima could evaluate this function for
Note that Maxima translates input x!! into an noun form
genfact (x, x/2, 2).