CauchyFormeln
Cauchyformeln, also known as Cauchy's integral formulas, are fundamental results in complex analysis named after Augustin-Louis Cauchy. These formulas provide a means to evaluate complex integrals and are central to the theory of holomorphic functions.
The principal Cauchy integral formula states that if a function \(f\) is holomorphic inside and on a
\[
f(a) = \frac{1}{2\pi i} \int_C \frac{f(z)}{z - a} \, dz
\]
This formula not only allows the computation of function values but also leads to various derivatives’ formulas.
\[
f^{(n)}(a) = \frac{n!}{2\pi i} \int_C \frac{f(z)}{(z - a)^{n+1}} \, dz
\]
Cauchy’s integral formulas are vital for establishing the properties of holomorphic functions, including their analytic continuation
In summary, Cauchyformeln provide a powerful tool for evaluating and understanding functions of a complex variable,