In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood...

analysis, a complex-valued function f {\displaystyle f} of a complex variable z {\displaystyle z} : is said to be holomorphic at a point a {\displaystyle...

heading. As in complex analysis of functions of one variable, which is the case n = 1, the functions studied are holomorphic or complex analytic so that, locally...

analytic functions are exactly equivalent to holomorphic functions, and are thus much more easily characterized. For the case of an analytic function with...

complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a set of isolated...

antiholomorphic functions (also called antianalytic functions) are a family of functions closely related to but distinct from holomorphic functions. A function of...

concerned with analytic functions of a complex variable, that is, holomorphic functions. The concept can be extended to functions of several complex variables...

\gamma ^{*}(s,z),} extends the real lower incomplete gamma function as a holomorphic function, both jointly and separately in z and s. It follows from the...

on this class of functions. In several ways, the harmonic functions are real analogues to holomorphic functions. All harmonic functions are analytic, that...

central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary...