In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain. The existence of a complex derivative is a very strong condition, for it implies that any holomorphic function is actually infinitely differentiable and equal to its own Taylor series.

En analyse complexe, une fonction holomorphe est une fonction à valeurs dans , définie et dérivable en tout point d'un sous-ensemble ouvert du plan complexe .

Funkcja analityczna – rodzaj funkcji rozważanej w analizie zespolonej.

Le funzioni olomorfe sono gli oggetti principali degli studi dell'analisi complessa; esse sono funzioni definite su un sottoinsieme aperto del piano dei numeri complessi  con valori in che sono differenziabili in senso complesso in ogni punto del loro dominio.