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The explicit formula for the antiderivative $F(z)$ of a holomorphic function $f$ on a domain $D$ is given by the contour integral of $f(w)$ along a path $\gamma_z$ from a fixed base point $z_0$ to $z$. The formula is $F(z) := \int_{\gamma_z} f(w) dw$.

Conditions: The function f is holomorphic on the domain D.; The domain D is simply connected (ensuring path independence).; A base point $z_0$ is fixed in D.; $\gamma_z$ is a path in D from $z_0$ to z.

The explicit formula for the antiderivative $F(z)$ of a holomorphic function $f$ on a domain $D$ is given by the contour integral of $f(w)$ along a path $\gamma_z$ from a fixed base point $z_0$ to $z$. The formula is $F(z) := \int_{\gamma_z} f(w) dw$.

Conditions: The function f is holomorphic on the domain D.; The domain D is simply connected (ensuring path independence).; A base point $z_0$ is fixed in D.; $\gamma_z$ is a path in D from $z_0$ to z.