Product (∏) in LaTeX
\prod produces the product operator, the multiplicative counterpart of \sum. The index goes in the subscript and the upper limit in the superscript.
LaTeX command
\prodNot the symbol you meant? Draw it to find the command →
Write a product as \prod_{k=1}^{n} a_k, exactly as you would a sum: index below with _, upper limit above with ^, and braces around any multi-character limit. It is ideal for factorials (n! = \prod_{k=1}^{n} k) and infinite products.
Limit placement follows the mode. In a displayed equation the limits stack above and below; inline they move beside the sign and it shrinks. Use \displaystyle\prod or \prod\limits to keep them stacked within a line, and \prod\nolimits to force the side form.
Use \prod, the large operator, rather than \Pi, the Greek capital, so the spacing and limits are right. The related coproduct is \coprod. Remember the empty product convention: a product with no factors equals 1, which matters when the lower limit exceeds the upper.
Examples
$n! = \prod_{k=1}^{n} k$factorial as a product
$\prod_{i=1}^{n} x_i$a product of terms
$\prod_{p} \frac{1}{1 - p^{-s}} = \zeta(s)$an Euler product
$\displaystyle\prod_{k=1}^{n} a_k$display size inline
$\coprod_{i \in I} X_i$a coproduct
Tips and common mistakes
- Add bounds with _ and ^ just like
\sum:\prod_{k=1}^{n}. Brace multi-character limits. - Inline, the limits move beside the sign and it shrinks; use
\displaystyle\prodor\prod\limitsto stack them. - Use
\prod, not\Pi; the Greek capital has the wrong spacing and no movable limits. \coprodgives the coproduct and takes limits the same way.- Recall the empty-product convention equals 1 when the lower limit exceeds the upper.
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Convert your maths to LaTeX →FAQ
What is the LaTeX command for the product symbol?
\prod, which renders the large product operator with movable limits: .
How is \prod different from \Pi?
\prod is the large product operator carrying limits and correct spacing; \Pi is only the uppercase Greek letter. Use \prod for products.
Why do my product limits appear to the side?
Inline math places them beside the symbol. Switch to a displayed equation or write \displaystyle\prod (or \prod\limits) to stack them.