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# Variable size symbols

The size of some mathematical symbols, notably summation signs, product signs, and
integral signs, depends on the environment in which they
appear (i.e., `displaymath` as opposed to `math` environments;
see Math Formulas and
Math Fonts and Styles).
These include

`\sum` a summation sign (capital sigma)
`\prod` a product (capital pi)
`\coprod` a coproduct (inverted capital pi)
`\int` an integral sign
`\oint` a surface (circular) integral sign
`\bigcup` big "U"
`\bigcap` big inverted "U"
`\bigvee` big "V"
`\bigwedge` big inverted "V"
`\bigodot` big "O" with dot at center
`\bigotimes` big "O" with cross inside
`\bigoplus` big "O" with a + inside
`\biguplus` big "U" with a + inside

The `\sqrt` command also produces a variable
size symbol appropriate for the size of hte radicand argument.

The "limits" associated with these symbols are entered as
subscripts for entries appearing below the
symbol and as superscripts for entries appearing
above the symbol.
For example the sum from n=0 to infinity of x_{n} would be entered as

\sum_{n=0}^{\infty} x_{n}

The actual placement of the limits depends on whether this
is in `displaymath` mode in which case they are placed below/above
or in `math` mode in running text in which case they are placed as regular
subscripts and superscripts.
Note that it is possible to treat several of these symbols (a common example
would be a double sum) as a single symbol for placing limits above and/or
below by using the `\mathop` command.

"Hats" and "tildes" over symbols which stretch (as best they can) to
the correct size for their arguments are produced by
`\widehat` and `\widetilde`.

Related topics:
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Revised: Sheldon Green, 28 Nov 1995.