# Uses for esoteric integral symbols

A while ago, I was searching for a TeX package which would provide a double integral symbol with a circle which I could use to typeset some lecture notes on surface integrals. I happened upon the esint package, which includes several integral symbols I had never seen before. In particular, integral symbols with a square (\sqint and \sqiint), a sloped dash (\fint) and the very curious \landupint and \landdownint. Is anyone familiar with any uses for these symbols?

Added (TB) Here's an image of the integral signs in question:

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The one with the sloped dash is sometimes used to denote integral averages:

\fint_A $f(x)d\mu(x) = \frac{1}{\mu(A)} \int_{A} f(x) d\mu(x)$

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Well, \sqint is the quaternion integral and \fint is used for integral averages, if memory serves. I'll have to look around for the others, though.

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The circles with arrows are useful for contour-integrals in complex analysis.

The \landupint and \landdonwint are probably used to expres contourintegrals that go around a singularity by integrating around the boundary of half of a circle ($\partial B(x,\epsilon)$) and letting $\epsilon\to 0$. I've never seen that symbol being used in practice, but it's what the picture suggests.

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