Antiderivative (complex analysis)

In complex analysis, a branch of mathematics, the antiderivative, or primitive, of a complex-valued function g is a function whose complex derivative is g. More precisely, given an open set ${\displaystyle U}$ in the complex plane and a function ${\displaystyle g:U\to \mathbb {C} ,}$ the antiderivative of ${\displaystyle g}$ is a function ${\displaystyle f:U\to \mathbb {C} }$ that satisfies ${\displaystyle {\frac {df}{dz}}=g}$.

As such, this concept is the complex-variable version of the antiderivative of a real-valued function.