In mathematics, infinite-dimensional holomorphy is a branch of functional analysis. It is concerned with generalizations of the concept of holomorphic function to functions defined and taking values in complex Banach spaces (or Fréchet spaces more generally), typically of infinite dimension. It is one aspect of nonlinear functional analysis.
Read more about Infinite-dimensional Holomorphy: Vector-valued Holomorphic Functions Defined in The Complex Plane, Holomorphic Functions Between Banach Spaces, Holomorphic Functions Between Topological Vector Spaces