Uses for esoteric integral symbols

analysis notation

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

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


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.


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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