holomorphic
Let be a domain in the complex numbers. A function is holomorphic if has a complex derivative at every point in , i.e. if
exists for all .
More generally, if is a domain, then a function is said to be holomorphic if is holomorphic in each of the variables. The class of all holomorphic functions on is usually denoted by .
Title | holomorphic |
Canonical name | Holomorphic |
Date of creation | 2013-03-22 12:04:33 |
Last modified on | 2013-03-22 12:04:33 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 12 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 30D20 |
Classification | msc 32A10 |
Synonym | holomorphic function |
Synonym | regular function |
Synonym | complex differentiable |
Related topic | CauchyRiemannEquations |
Related topic | Analytic |