Adjective
(complex analysis, of a complex function) Complex-differentiable on an open set around every point in its domain.
Having holohedral symmetry.
Source: en.wiktionary.orgA simple converse is that if u and v have continuous first partial derivatives and satisfy the Cauchy–Riemann equations, then f is holomorphic. Source: Internet
Being one-to-one and holomorphic implies having a non-zero derivative. Source: Internet
As a holomorphic function, the Laplace transform has a power series representation. Source: Internet
Connection with holomorphic functions Solutions of the Laplace equation in two dimensions are intimately connected with analytic functions of a complex variable (a. Source: Internet
A variation of this proof does not require the use of the maximum modulus principle (in fact, the same argument with minor changes also gives a proof of the maximum modulus principle for holomorphic functions). Source: Internet
All holomorphic functions are complex-analytic. Source: Internet