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I am typesetting an equation of the form $$\sum_{i=1}^n\Bigl(x_i \prod_{j=1}^i(y_j + \alpha) \Bigr)$$ Originally, I wrote the equation without the outer pair of parentheses, and a reviewer asked me to include them. I agree that they improve the legibility of the equation. But are these parentheses strictly necessary?

In my opinion, the fact that the inner product depends on $i$ rules out any alternative interpretation of $$\sum_{i=1}^n x_i \prod_{j=1}^i(y_j + \alpha) $$ For that reason, my preference is to include the outer parentheses on the first mention and exclude them from subsequent uses of this equation. Is this a reasonable solution?

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Max
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    As you mentioned, the parentheses are not strictly necessary, but I would include them anyway. If you do that, you draw the attention to the fact that the upper limit in the product depends on $i$. – Andrei Feb 21 '22 at 04:48
  • If you’re going to use parentheses here, you should use \left( and \right) to size them properly. – RobPratt Feb 21 '22 at 06:10
  • I’m voting to close this question because it's not about mathematics. That said, I say keep the parentheses everywhere. That makes life easier for your readers, which is the purpose of good notation. – Ethan Bolker Feb 21 '22 at 23:01
  • @EthanBolker There are currently 11,500 questions in the [notation] tag on this site. If you think that this tag is off-topic, then this is an issue for meta. – Max Feb 21 '22 at 23:51
  • @RobPratt, I am reverting your spurious edit changing "parentheses" to "brackets" in my title. Changing American usage to British usage and vice-versa is considered bad practice on this site: meta link 1 meta link 2 – Max Feb 21 '22 at 23:51
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    @Max I didn’t change to brackets. I corrected $y_i$ to $y_j$. – RobPratt Feb 21 '22 at 23:59
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    @RobPratt Indeed, I am a fool: I had made the change myself and forgotten about it. My apologies. – Max Feb 22 '22 at 00:03
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    No problem. I am American, so I would have changed it from brackets. :) – RobPratt Feb 22 '22 at 00:08

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