This page gathers the 23 dictionary entries belonging to the domain “Complex analysis”, as labelled by Wiktionary. Each word leads to its full entry: definitions, etymology, pronunciation, examples.
- Ahlfors theory noun A geometric counterpart to Nevanlinna theory that extends the applicability of the concept of covering surface (of a topological space) by…
- bilinear adj Of or pertaining to a Möbius transformation (type of conformal map representable as the ratio of two linear functions).
- branch cut noun A curve in the complex plane such that it is possible to define a single analytic branch of a multi-valued function on the plane minus that…
- Cauchy-Riemann equation noun Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations…
- entire adj Complex-differentiable on all of ℂ.
- holomorphic adj Complex-differentiable on an open set around every point in its domain.
- imaginary number noun A number of the form bi, where b is any real number and i denotes the imaginary unit.
- imaginary unit noun An imaginary number (in the case of complex numbers, usually denoted i) that is defined as a solution to the equation x²=-1.
- meromorphic adj That is the ratio of two holomorphic functions (and so possibly infinite at a discrete set of points).
- Mittag-Leffler star noun A set in the complex plane obtained by attempting to extend a given complex-analytic function along rays emanating from a given point.
- Mittag-Leffler summation noun Any of several variations of the Borel summation method for summing possibly divergent formal power series.
- Möbius transformation noun A transformation of the extended complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are…
- Nevanlinna theory noun A part of the theory of meromorphic functions that describes the asymptotic distribution of solutions to the equation ƒ(z) = a, as a varies.
- normal adj Which is pre-compact.
- pole noun For a meromorphic function f(z), any point a for which f(z)→∞ as z→a.
- rational function noun Any function expressible as the quotient of two (coprime) polynomials (and which thus has poles at a finite, discrete set of points which…
- residue noun A form of complex number, proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities.
- Riemann sphere noun The complex numbers extended with the number ∞; the complex plane (representation of the complex numbers as a Euclidean plane) extended…
- Schwarz-Christoffel mapping noun A conformal map of the upper half-plane or the complex unit disk onto the interior of a simple polygon; used in minimal surfaces…
- stereographic projection noun A function that maps a sphere onto a plane; especially, the map generated by projecting each point of the sphere from the sphere's…
- transcendental function noun A meromorphic function on the complex plane that is not a rational function.
- univalent adj (Holomorphic and) injective.
- vinculum noun A horizontal line placed over a complex number or expression to denote its complex conjugate.