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I have a series of terms $\{t_n : t_n = a_n x_n\}$, and I want to talk about the product of each term except $t_j$.

Would any of these be an appropriate way to say that? I like this:

$\prod_{i \ne j} t_i$

or maybe this

$\prod_{i=1,i \ne j}^n t_i$

Is it a normal thing to do, to put qualifiers on an index like that, or is there a better way to do it?

Or would it be better to make a subset, $\{b_n : a_n, n \ne j \}$ and use that:

$\prod_{i=1}^n b_i$

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    In addition to the fact that it is complicated (as Matt E pointed out), I do not think that the third suggestion is even correct. It still denotes the product of the n numbers $b_1,\ldots,b_n$, which is not defined unless you specify the value of $b_j$.2010-09-23

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It is normal to write

$\prod_{\begin{matrix}i=1 \\ i \ne j \end{matrix}}^n t_i$

but another good notation is

$\prod_{t \in T \setminus \{t_j\}} t$

(with $T = \{t_n : t_n = a_n x_n\}$, also note that it is only defined up to permutation)

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    @Rahul: Well they could just write t_(n-i) instead of t_i2010-09-23
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$\large{\text{Annex to Tsuyoshi Ito's Comment :}}$

I thought to provide some more detail. User Unkz defined: $b_n:= a_n, \forall \; n \neq j$. So $\color{red}{b_j}$ doesn't exist.

However, by definition of the Pi notation: $\prod_{i=1}^n b_i := b_1b_2...b_{j-1}\color{red}{b_j}b_{j+1}...b_n$.
Since $\color{red}{b_j}$ doesn't exist but this product contains $\color{red}{b_j}$, therefore this product cannot exist either.