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Cauchy’s
auchy’s integral formula is a fundamental result in complex analysis providing a powerful method for evaluating integrals ofomorphic functions. It states that if (f) is a complex function holomorphic within and on a simple closed (C), and (a) is a point inside (C), then:
\[f(a) = \frac{1}{2pi} \oint \frac{f(z{z - a} \, dz\]
This formula allows the value of the function at point inside the to be expressed as an over boundary, establishing a direct link between boundary values and interior values of holomorphic functions.