https://en.wikipedia.org/wiki/Holomorphic_function Holomorphic function (抜粋) For Zariski's theory of holomorphic functions on an algebraic variety, see formal holomorphic function.
In mathematics, 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 in a neighborhood is a very strong condition, for it implies that any holomorphic function is actually infinitely differentiable and equal to its own Taylor series (analytic). Holomorphic functions are the central objects of study in complex analysis. (引用終り)
