Torus integral

Summary

The torus integral of a function $f$ on $\C^n$ is the iterated contour integral of $f(\zeta) \, d\zeta_1 \cdots d\zeta_n$ over a product of $n$ circles. This product is the distinguished boundary of a polydisc. It is computed by parametrising each circle by an angle and integrating over the cube $[0, 2\pi]^n$. It appears in the Cauchy integral formula on a polydisc. It also gives the coefficients of a power series in several variables. For $n = 1$ it is the contour integral over a circle.