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A '''discontinuous group''' is a mathematical concept relating to mappings in [[topological space]]. ...[[transitive relation|transitive]] group of [[homeomorphism|homeomorphic]] mappings of <math>T</math> on itself. The representation <math>\tau\to f(\tau,a)</ma ...

...cal proofs that [[limit of a sequence|sequences]] or [[limit of a function|functions]] converge to a finite [[limit (mathematics)|limit]] when the argument tend ...propriate techniques. The links below give details of necessary conditions and generalizations to more abstract settings. Proof techniques for the converg ...

...onogenic at <math> \zeta \in A </math>, if <math> f'(\zeta) </math> exists and is finite, with: ...ains can also be generalized <ref name='ency_math'/> in a manner such that functions which are monogenic over non-connected subsets of <math> \mathbb{C} </math> ...

{{Short description|Type of functions in algebra}} where the <math>\lambda_{i_j}: V \to k</math> are linear functionals and the <math>w_{i_1, \dots, i_n}</math> are vectors in ''W''. For example, if ...

...ic vector field on the disk given by a one parameter family of holomorphic functions on the disk with positive real part. The Loewner semigroup generalizes the ...n the late 1990s, has been extensively developed in [[probability theory]] and [[conformal field theory]]. ...

...cess-date=8 February 2023}}</ref> For example, for the family of quadratic functions having the general form and every quadratic may be converted to that form by translations and dilations, which may be seen by [[completing the square]]. ...

...|an open set covering of the [[sierpinski triangle]] along with one of its mappings ψ_''i''.]] ...iven an [[iterated function system]] of [[contraction mapping| contractive mappings]] <math>\psi_1, \ldots, \psi_m</math>, the open set condition requires that ...

...doi=10.1080/00029890.1959.11989422}}</ref> The two most famous pseudogamma functions are [[Hadamard's gamma function]], where <math>\Phi</math> is the [[Lerch zeta function]], and the Luschny factorial:<ref>{{cite web |last1=Luschny |title=Is the Gamma fu ...

...idem Aşçıoğlu |date=September 2015 |title=The Generalized Incomplete Gamma Functions |publisher=Eastern Mediterranean University |s2cid=126117454 |url=https://p ...Library of Mathematical Functions]]<ref>{{dlmf|id=11.10|title=Anger-Weber Functions|first=R. B. |last=Paris}}</ref> can related: ...

...th>\Phi(x, y) = (\phi(x, y), y)</math> with <math>x \in V, y \in W</math>, and a smooth function ''h'' on ''W'' such that ...e extensions to infinite dimensions, to [[complex analytic function]]s, to functions invariant under the [[group action|action]] of a [[compact group]], ... ...

...of a bell-shaped function is typically a [[sigmoid function]]. Bell shaped functions are also commonly symmetric. Many common probability distribution functions are bell curves. ...

Coinage of the term 'ridge function' is often attributed to B.F. Logan and L.A. Shepp.<ref>{{cite journal |last1=Logan |first1=B.F. |last2=Shepp |firs ...arious estimation problems. This is a direct result of the fact that ridge functions are constant in <math>d-1</math> directions: ...

...'''primitive recursive set functions''' or '''primitive recursive ordinal functions''' are analogs of [[primitive recursive function]]s, defined for [[Set (mat ...basic functions by repeatedly applying the following rules of substitution and recursion: ...

...one, then it is [[conformal map|conformal]]; if the distortion is bounded and the function is a [[homeomorphism]], then it is [[quasiconformal mapping|qu ...erminant]] J(''x'',ƒ) is locally integrable and does not change sign in Ω, and there is a measurable function ''K''(''x'')&nbsp;≥&nbsp;1 such that ...

...elf to have a fixed point. The result was proved in 1968 by Clifford Earle and [[Richard S. Hamilton]] by showing that, with respect to the [[Carathéodory Let ''D'' be a connected open subset of a complex [[Banach space]] ''X'' and let ''f'' be a holomorphic mapping of ''D'' into itself such that: ...

...analytic]]) functions of one complex variable is one of the most beautiful and most useful parts of the whole mathematics. ...maps between two-dimensional spaces ([[Riemann surfaces]]). The theory of functions ...

...izing the derivative of a complex-valued function as a local amplification and twist of vectors at a point in the complex plane.<ref name=":0" /><ref>{{ci [[Category:Functions and mappings]] ...

...turally in manifold-constrained problems in the [[calculus of variations]] and [[partial differential equation]]s, including the theory of [[harmonic map] ...=Hang |first1=Fengbo |last2=Lin |first2=Fanghua |title=Topology of sobolev mappings, II |journal=Acta Mathematica |date=2003 |volume=191 |issue=1 |pages=55–107 ...

...riptstyle\mathcal{K}</math>-equivalent if ''&fnof;''^&minus;1(0) and ''g''^&minus;1(0) are [[diffeomorphic]]. :<math>\Psi(x,0) = (\varphi(x), 0)</math>, and ...

...andard notation for the family of subsets with a given order type. Jónsson functions are named for [[Bjarni Jónsson]]. ...for this special case there is a simpler proof of the existence of Jónsson functions. {{harvs|txt|authorlink=Fred Galvin|last=Galvin|last2= Prikry|year=1976}} g ...