Complex analysis

expression of a function as an infinite sum

branch of mathematics studying functions of a complex variable

infinite sum of monomials

geometric representation of the complex numbers

definite integral of a scalar or vector field along a path

power series generalized to allow negative powers

system of linear partial differential equations characterizing holomorphic (complex differentiable) functions

isolated singularity of a holomorphic function 𝑓 such that 1/𝑓 has a zero and is holomorphic at the singularity

coefficient of the term of order −1 in the Laurent expansion of a function holomorphic outside a point, whose value can be extracted by a contour integral

function or sequence whose possible values form a bounded set

angle of complex number about real axis

mathematical operation

Taylor series

number of times a curve wraps around a point in the plane

ratio of a function's derivative to the function; d(ln|f(x)|)/dx

concept in mathematics

isolated singularity that is neither removable nor a pole

relations connecting the real and imaginary parts of any complex function that is analytic in the upper half-plane

series which gives an approximation to a function as the argument tends to some point

isolated singularity is one that has no other singularities close to it

technique for visualizing complex functions

thumb|The imaginary part of the complex logarithm. Trying to define the complex logarithm on \C-\{0\} gives different answers along different paths. This leads to an infinite cyclic monodromy group and a covering of \C-\{0\} by a [[helicoid (an example of a Riemann surface).]]

point of interest for complex multi-valued functions

space of holomorphic functions on the unit disk or upper half plane

method of evaluating certain integrals along paths in the complex plane

the inverse operation to the Laplace transform

function that "converges" to periodicity

complex numbers with positive imaginary part

function f such that, if f≤h on the boundary of a ball for any harmonic function h, then f≤h also inside the ball

branch of mathematics about iteration of complex-valued functions

bimodal function

inequality applying to sequences of complex numbers

Function family in complex analysis

In mathematics, hyperfunctions are generalizations of functions, as a 'jump' from one holomorphic function to another at a boundary, and can be thought of informally as distributions of infinite order. Hyperfunctions were introduced by Mikio Sato in 1958 in Japanese, (1959, 1960 in English), building upon earlier work by Laurent Schwartz, Grothendieck and others.

mathematical function

conformally invariant stochastic process

technique of studying linear partial differential equations

collection of continuous functions

values along one branch of a multivalued function so that it is single-valued

annual mathematics award

branching out of a mathematical structure

type of graph drawing used to study Riemann surfaces

linear partial differential operators (first order constant coefficients) on f(ℂⁿ or ℝ²ⁿ)

holomorphic function with growth bounded by an exponential function

mathematical integral

nonlinear differential operator used to study conformal mappings

concept in complex analysis

way of writing a meromorphic function

creating a meromorphic function in multiple variables

method for visualizing vector fields

concept in differential equation mathematics

mathematical theorem

function which selects one section of a multi-valued function

homeomorphism between plane domains