Notation for infinite product in reverse order This question is related to notation of infinite product. 
We know that,
$$
\prod_{i=1}^{\infty}x_{i}=x_{1}x_{2}x_{3}\cdots
$$
How do I denote
$$
    \cdots x_{3}x_{2}x_{1}  ?   
$$
One approach could be 
$$
\prod_{i=\infty}^{1}x_{i}=\cdots x_{3}x_{2}x_{1}
$$
I need to use this expression in a bigger expression so I need a good notation for this. Thank you in advance for your help. 
 A: Is there any reason to avoid the obvious $\;\; \displaystyle\prod_{i=-\infty}^{-1} x_{-i} \;\;$ ?

(as opposed to dropping the negative signs, like in the approach you suggested)

A: Sometimes in Clifford algebra when they do products backwards they talk of the "reverse" of the product. I've seen this denoted various ways with tidles: $\widetilde{abc}=cba$ or $(abc)^{\sim}=cba$. If you like them you could consider 
$$\widetilde{\Pi_{i=1}^\infty a_i}$$ or $$(\Pi_{i=1}^\infty a_i)^\sim$$
A: If they’re matrices, you can of course simply use $$\left(\prod_{n\ge 0}x_n^T\right)^T\;.$$
A: In the theory of non-autonomous abstract evolution equations, it is quite costumary to use the followiong notation:
For a family of operators
$U_0,U_1,\ldots,U_{n-1}\in\mathcal{L}(X)$, we denote the "time-ordered"
product of these operators by
\begin{equation*}
\prod_{p=0}^{n-1}U_p:=U_{n-1} U_{n-2} \cdots U_1
U_0\quad\mbox{and}\quad\prod_{p=n-1}^{0}U_p:=U_0U_1\cdots U_{n-2}
U_{n-1} .
\end{equation*}
See Pazy, Page 130.
A: (With tongue in cheek:) what about this?
$$\left(x_n\prod_{i=1}^\infty \right)\;$$
