Cauchy's integral formula

Provides integral formulas for all derivatives of a holomorphic function

From Cauchy's inequality, one can easily deduce that every bounded entire function must be constant (which is Liouville's theorem).

It is this useful property that can be used, in conjunction with the generalized Stokes theorem:

Thus, as in the two-dimensional (complex analysis) case, the value of an analytic (monogenic) function at a point can be found by an integral over the surface surrounding the point, and this is valid not only for scalar functions but vector and general multivector functions as well.