f: U ⊆ ℂ → ℂ is holomorphic iff it is complex-differentiable at every point of U. Equivalently (on open sets): analytic, i.e. locally given by a convergent power series.
Holomorphic function
Related concepts
- Complex numbers (ℂ)
- Derivative
- Cauchy-Riemann equations
- Cauchy integral formula
- Laurent series
- Analytic continuation
- Riemann mapping theorem
- Kähler manifold
- Modular form
- Liouville's theorem (complex analysis)
- Schwarz lemma
- Meromorphic function
- Riemann surface
- Maximum modulus principle
- Möbius transformation
- Uniformisation theorem
- Maximum modulus principle
- Riemann mapping theorem
- Weierstrass factorization theorem
- Conformal mapping