Bug introduced in 9.0 or earlier and fixed in 11.0.0
This infinite product is correct:
Product[1/(1 - 1/2^n), {n, 1, Infinity}]
(* 1/QPochhammer[1/2, 1/2] *)
Numerical value of this result is not equal to zero
N[1/QPochhammer[1/2, 1/2]]
(* 3.462746619455064 *)
But from following equivalent expression I get a wrong output:
Product[1/(1 - 1/2^(n-1)), {n, 2, Infinity}]
(* 0 *)
1/(2 QPochhammer[1/2, 1/2])
, as it should be. $\endgroup$ – bbgodfrey Dec 19 '15 at 17:1810.0 for Microsoft Windows (64-bit)
with Windows 8.1 $\endgroup$ – mattiav27 Dec 19 '15 at 17:210/QPochhammer[2, 1/2]
on 10.3.1. $\endgroup$ – b.gates.you.know.what Dec 19 '15 at 17:24Infinity
to some large integer instead, it evaluates correctly. $\endgroup$ – march Dec 19 '15 at 17:48