Editing Cauchy's integral formula (section)

===Several variables===
In [[Function of several complex variables|several complex variables]], the Cauchy integral formula can be generalized to [[polydisc]]s.<ref>{{harvnb|Hörmander|1966|loc=Theorem 2.2.1}}</ref>  Let {{math|''D''}} be the polydisc given as the [[Cartesian product]] of {{math|''n''}} open discs {{math|''D''<sub>1</sub>, ..., ''D''<sub>''n''</sub>}}:
<math display="block">D = \prod_{i=1}^n D_i.</math>

Suppose that {{math|''f''}} is a holomorphic function in {{math|''D''}} continuous on the closure of {{math|''D''}}.  Then
<math display="block">f(\zeta) = \frac{1}{\left(2\pi i\right)^n}\int\cdots\iint_{\partial D_1\times\cdots\times\partial D_n} \frac{f(z_1,\ldots,z_n)}{(z_1-\zeta_1)\cdots(z_n-\zeta_n)} \, dz_1\cdots dz_n</math>
where {{math|1=''ζ'' = (''ζ''<sub>1</sub>,...,''ζ''<sub>''n''</sub>) ∈ ''D''}}.