31 - The Cauchy Integral Formula

Suppose that we have a bounded regular domain and a function holomorphic on that domain, then,

The Cauchy Integral Formula for Derivatives

Suppose that we once again have a bounded regular domain and a function holomorphic on , then every -th derivative exists and is given by

Holomorphic functions are infinitely differentiable

From the above, we find that holomorphic functions over an open domain are infinitely differentiable on that domain, and so are their composing real and imaginary parts.