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I'm looking for a symbol that merges \iint and \oint together (a dedicated package, if it could exist, would provide something like \oiint and \oiiint).

The purpose of \oint is to show that the integration path is closed (it is often used in the definition of the circulation), but the adding one (or two) more integral it is emphasized that the integral is calculated over a surface (\oiint) or over a volume (\oiiint).

Do these symbols exist in the world of LaTeX?

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Have a look at “How to look up a math symbol?” for ideas how you can easily find a particular symbol. –  Caramdir Sep 23 '10 at 15:09
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up vote 5 down vote accepted

wasysym, txfonts, and pxfonts packages provide these symbols. It is always a good idea to check the comprehensive latex symbol list

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