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Undefined point on a holomorphic function which can be made regular
isolated singularities can be completely classified. A holomorphic function's singularity is either not really a singularity at all, i.e. a removable singularity
Removable_singularity
Location around which a function displays irregular behavior
called an essential singularity of the function f {\displaystyle f} if the singularity is neither a pole nor a removable singularity. For example, the function
Essential_singularity
Attribute of a mathematical function
\over z(z-1)}} it is apparent that the singularity at z = 0 {\displaystyle z=0} is a removable singularity and then the residue at z = 0 {\displaystyle
Residue_(complex_analysis)
Concept of complex analysis
{\displaystyle f} is either analytic at c {\displaystyle c} or has a removable singularity there. If the limit is equal to infinity, then the order of the
Residue_theorem
Has no other singularities close to it
function, then a {\displaystyle a} is an isolated singularity of f {\displaystyle f} . Every singularity of a meromorphic function on an open subset U
Isolated_singularity
Point where a mathematical object behaves irregularly
function. A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame, which can be removed by choosing a different
Singularity_(mathematics)
Topics referred to by the same term
dentistry Removable User Identity Module (R-UIM), telecommunication In mathematical analysis Removable discontinuity Removable set Removable singularity Removal
Removable
Theorem about the range of an analytic function
Picard's Theorem: If an analytic function f {\textstyle f} has an essential singularity at a point w {\textstyle w} , then on any punctured neighborhood of w
Picard_theorem
Concept in complex analysis
certain type of singularity of a complex-valued function of a complex variable. It is the simplest type of non-removable singularity of such a function
Zeros_and_poles
Theorem
the center a {\displaystyle a} to the nearest non-removable singularity; if there are no singularities (i.e., if f {\displaystyle f} is an entire function)
Analyticity of holomorphic functions
Analyticity_of_holomorphic_functions
Mathematical theory
mathematical singularity as a value at which a function is not defined. For that, see for example isolated singularity, essential singularity, removable singularity
Singularity_theory
Mathematical analysis of discontinuous points
{\displaystyle x=x_{0}.} The term removable discontinuity is sometimes broadened to include a removable singularity, in which the limits in both directions
Classification of discontinuities
Classification_of_discontinuities
Theorem in complex analysis
∞ {\displaystyle \infty } , then ∞ {\displaystyle \infty } is a removable singularity of f {\displaystyle f} , i.e. f {\displaystyle f} cannot blow up
Liouville's theorem (complex analysis)
Liouville's_theorem_(complex_analysis)
Partial differential equations whose solutions are instantons
in Mathematical Physics, 83(1), 31–42. Uhlenbeck, K. K. (1982). Removable singularities in Yang–Mills fields. Communications in Mathematical Physics, 83(1)
Yang–Mills_equations
Special mathematical function defined as sin(x)/x
a factor of π. In both cases, the value of the function at the removable singularity at zero is understood to be the limit value 1. The sinc function
Sinc_function
Provides integral formulas for all derivatives of a holomorphic function
. This is analytic (since the contour does not contain the other singularity). We can simplify f 1 {\displaystyle f_{1}} to be: f 1 ( z ) = z 2 z
Cauchy's_integral_formula
Branch of mathematics studying functions of a complex variable
applicable (see methods of contour integration). A "pole" (or isolated singularity) of a function is a point where the function's value becomes unbounded
Complex_analysis
Condition in which spacetime itself breaks down
A gravitational singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that
Gravitational_singularity
Complex-differentiable (mathematical) function
Basic theory Argument principle Residue Essential singularity Isolated singularity Removable singularity Zeros and poles Complex functions Complex-valued
Holomorphic_function
Mathematical theorem
then z0 is a removable singularity of f . Both possibilities contradict the assumption that the point z0 is an essential singularity of the function
Casorati–Weierstrass_theorem
Type of function in mathematics
{\displaystyle 1} , because the nearest singularity is at z = − 1 {\displaystyle z=-1} . Complex singularities can determine the radius of convergence
Analytic_function
Power series with negative powers
f(x)} for all x ∈ C {\displaystyle x\in \mathbb {C} } except at the singularity x = 0 {\displaystyle x=0} . The graph on the right shows f ( x ) {\displaystyle
Laurent_series
Mathematical function that preserves angles
often used to try to make models amenable to extension beyond curvature singularities, for example to permit description of the universe even before the Big
Conformal_map
Key results in general relativity on gravitational singularities
Big Bang singularity and the typical singularity inside a non-rotating, uncharged Schwarzschild black hole are spacelike. Timelike singularities: These
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Theorem in complex analysis
z-z_{Z}}+{g'(z) \over g(z)}.} Since g(zZ) ≠ 0, it follows that g' (z)/g(z) has no singularities at zZ, and thus is analytic at zZ, which implies that the residue of
Argument_principle
Second-order partial differential equation
only valid locally, or provided that the path does not loop around a singularity. For example, if r and θ are polar coordinates and φ = log r , {\displaystyle
Laplace's_equation
Mathematical theorem in complex analysis
function f ( z ) − p a ( z ) {\displaystyle f(z)-p_{a}(z)} has only a removable singularity at a {\displaystyle a} ; in particular, the principal part of f
Mittag-Leffler's_theorem
Functions in mathematics
harmonic function with the same singularity, so in this case the harmonic function is not determined by its singularities; however, we can make the solution
Harmonic_function
Characteristic property of holomorphic functions
Basic theory Argument principle Residue Essential singularity Isolated singularity Removable singularity Zeros and poles Complex functions Complex-valued
Cauchy–Riemann_equations
Experimental operating system from Microsoft Research
Team (video & thread). Singularity IV: Return of the UI, a demo of Singularity actually running (video & thread). Singularity Revisited, an interview
Singularity (operating system)
Singularity_(operating_system)
Domain of convergence of power series
At z = 0, there is in effect no singularity since the singularity is removable. The only non-removable singularities are therefore located at the other
Radius_of_convergence
Class of mathematical function
singularity. The function f ( z ) = sin 1 z {\displaystyle f(z)=\sin {\frac {1}{z}}} is not meromorphic either, as it has an essential singularity at
Meromorphic_function
analysis) Residue (complex analysis) Isolated singularity Removable singularity Essential singularity Branch point Principal branch Weierstrass–Casorati
List of complex analysis topics
List_of_complex_analysis_topics
Singularities of holomorphic functions extend infinitely outward
direction. More precisely, it shows that an isolated singularity is always a removable singularity for any analytic function of n > 1 complex variables
Hartogs's_extension_theorem
Mathematical functions
definitions of the principal values, although the second one introduces a removable singularity at z = 0. The two definitions of artanh {\displaystyle \operatorname
Inverse_hyperbolic_functions
Mathematical theorem
{\displaystyle h(G_{2})} is C {\displaystyle \mathbb {C} } with a horizontal slit removed. So we have that h ( f ( z ) ) = z + ( a 1 + b 1 ) z − 1 + ⋯ , {\displaystyle
Riemann_mapping_theorem
Infinite sum that is considered independently from any notion of convergence
obtained by truncating the series at x n , {\displaystyle x^{n},} that is, by removing all terms involving a power of X {\displaystyle X} higher than n . {\displaystyle
Formal_power_series
Conformal mappings in complex analysis
regular singular points at z = 0, 1, and ∞, corresponding to the vertices of the triangle with angles πα, πγ, and πβ respectively. At these singular points
Schwarz_triangle_function
Type of analog linear filter in electronics
indeterminate by the definition of reverse Bessel polynomials, but is a removable singularity, it is defined that θ n ( 0 ) = lim x → 0 θ n ( x ) {\displaystyle
Bessel_filter
values 0 or ∞ at P, the definition is essentially in limiting or removable singularity terms, by considering (up to sign) fagb with a and b such that the
Weil_reciprocity_law
General relativity model near spacetime singularities
relativity has a page on the topic of: BKL singularity A Belinski–Khalatnikov–Lifshitz (BKL) singularity is a model of the dynamic evolution of the universe
BKL_singularity
Ratio of polynomial functions
f(x)={\tfrac {x}{x}}} is equal to 1 for all x except 0, where there is a removable singularity. The sum, product, or quotient (excepting division by the zero polynomial)
Rational_function
Riemann–Hurwitz formula Riemann matrix Riemann operator Riemann singularity theorem Riemann-Kempf singularity theorem Riemann surface Compact Riemann surface Planar
List of things named after Bernhard Riemann
List_of_things_named_after_Bernhard_Riemann
Singularity theorem in Yang–Mills theory
particular Yang–Mills theory, Uhlenbeck's singularity theorem is a result allowing the removal of a singularity of a four-dimensional Yang–Mills field with
Uhlenbeck's singularity theorem
Uhlenbeck's_singularity_theorem
2012 film
The Singularity is a 2012 documentary film about the technological singularity, produced and directed by Doug Wolens. The film has been called "a large-scale
The_Singularity_(film)
Expression which is not assigned an interpretation
function is undefined, is called a singularity. Some different types of singularities include: Removable singularities - in which the function can be extended
Undefined_(mathematics)
American computer scientist, author and futurist (born 1948)
book, The Singularity Is Nearer: When We Merge with AI, was published in 2024. In 2010, Kurzweil wrote and co-produced the film The Singularity Is Near:
Ray_Kurzweil
Annual conference
website The Singularity Summit at Stanford, 2006 The Singularity Summit Australia, 2012 The Singularity Summit Australia, 2011 The Singularity Summit Australia
Singularity_Summit
Concept in complex analysis
extension to all of Ω. By Riemann's theorem for removable singularities, every singleton is removable. This motivated Painlevé to pose a more general
Analytic_capacity
Matrix used in complex analysis
another derivation of the Grunsky inequalities using reproducing kernels and singular integral operators in geometric function theory; a more recent related
Grunsky_matrix
Point on a curve where motion must move backwards
type A2-singularity. Let f (x, y) be a smooth function of x and y and assume, for simplicity, that f (0, 0) = 0. Then a type A2-singularity of f at (0
Cusp_(singularity)
Analytic function in mathematics
Zbl 0315.10035. Trivial exceptions of values of s that cause removable singularities are not taken into account throughout this article. Neukirch, Jürgen
Riemann_zeta_function
On when a definite intersection form of a smooth 4-manifold is diagonalizable
obtains a unique singular ASD connection, which becomes a well-defined smooth ASD connection at that point using Uhlenbeck's singularity theorem. Donaldson
Donaldson's_theorem
Singularity or discontinuity only resulting from the choice of coordinate system
physics, a coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame that can be removed by choosing a different
Coordinate_singularity
Type of spacetime singularity in fiction
term quantum singularity is used to refer to many different phenomena in fiction. They often only approximate a gravitational singularity in the scientific
Quantum_singularity
Point without a tangent space
multiplicity two and the tangent cone is not singular outside its vertex. Milnor map Resolution of singularities Singularity theory Zariski tangent space Hartshorne
Singular point of an algebraic variety
Singular_point_of_an_algebraic_variety
American mathematician (born 1942)
aspects of mathematical gauge theory", based on her 1982 papers "Removable singularities in Yang–Mills fields"[RSY] and "Connections with bounds on curvature"
Karen_Uhlenbeck
Matrices satisfying a differential equation
{\displaystyle w,z,} which under suitable hypotheses is a curve, often after removing singularities. By the isospectral property, this curve is preserved under time
Lax_pair
Mathematical formula in complex analysis
F(z):={\frac {f(z)}{\prod _{k=1}^{n}(z-a_{k})}}} and fill in all the removable singularities. We obtain a function F {\displaystyle F} that is analytic in B
Jensen's_formula
Concept in algebraic geometry
does not is given by the isolated singularity of x2 + y3z + z3 = 0 at the origin. Blowing it up gives the singularity x2 + y2z + yz3 = 0. It is not immediately
Resolution_of_singularities
2013 studio album by Northlane
"Northlane Singularity". Rogers, Jack (22 April 2013). "Northlane – Singularity". Rock Sound Magazine. Retrieved 27 July 2019. "Album review – Singularity Northlane"
Singularity_(Northlane_album)
Programming language construct for special conditions
pre-substitution of a value followed by resumption, to concisely handle removable singularities. The default IEEE 754 exception handling behaviour of resumption
Exception_handling
Israeli-American physicist (1909–1995)
bimetric gravity, an attempt to improve on general relativity by removing singularities and replacing pseudotensors with tensors to eliminate nonlocality
Nathan_Rosen
Mathematical function
Intuitively, the singularity spectrum gives a value for how "fractal" a set of points are in a function. More formally, the singularity spectrum D ( α )
Singularity_spectrum
Description of the degeneracy of a function
In mathematics, and in particular singularity theory, an Ak singularity, where k ≥ 0 is an integer, describes a level of degeneracy of a function. The
Ak_singularity
evaluated at the singular configuration (if any exists), then those equations exhibit mathematical singularity. Examples of mechanical singularities are gimbal
Mechanical_singularity
Hypothetical object of spacetime
general relativity, a white hole is a hypothetical region of spacetime and singularity that cannot be entered from the outside, although energy, matter, light
White_hole
Harmonic functions as solutions to Laplace's equation
Laurent series, and the classification of singularities as removable, poles and essential singularities) generalize to results on harmonic functions
Potential_theory
Type of function
common for a function which contains a mathematical singularity to be referred to as a 'singular function'. This is especially true when referring to
Singular_function
Riemann's existence theorem (algebraic geometry) Riemann's theorem on removable singularities (complex analysis) Riemann–Roch theorem (Riemann surfaces, algebraic
List_of_theorems
Matrix decomposition
there is a universal constant that characterizes the regularity or singularity of a problem, which is the system's "condition number" κ := σ max / σ
Singular_value_decomposition
Concept in mathematics
In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to
Singular_perturbation
2003 science fiction novel by Charles Stross
Fools. Singularity Sky takes place roughly in the early 23rd century, around 150 years after an event referred to by the characters as the Singularity. Shortly
Singularity_Sky
Grammatical category
first-, second-, and third-person pronouns are typically also marked for singular and plural forms, and sometimes dual form as well (grammatical number)
Grammatical_person
Point at which time cannot be described mathematically
In theoretical physics, a chronometric singularity (also called a temporal or horological singularity) is a point at which time cannot be measured or described
Chronometric_singularity
Weather phenomenon occurring around the same time each year
In meteorology, a singularity is a weather phenomenon likely to occur with reasonable regularity around a specific approximate calendar date, outside
Singularity_(climate)
English mathematician, mathematical physicist (born 1931)
apparent singularity, similar to the well-known apparent singularity at the event horizon of a black hole. The latter singularity can be removed by a change
Roger_Penrose
Concept in algebraic topology
In algebraic topology, singular homology refers to the study of a certain set of algebraic invariants of a topological space X {\displaystyle X} , the
Singular_homology
American singer, songwriter, and actress (born 1999)
studio albums, Eyes Wide Open (2015), Evolution (2016), Singular: Act I (2018), and Singular: Act II (2019). Carpenter joined Island Records in 2021,
Sabrina_Carpenter
Awarded every year by the American Mathematical Society
27 (1): 199–245. ISSN 0065-1036. Uhlenbeck, Karen K. (1982). "Removable singularities in Yang-Mills fields". Communications in Mathematical Physics.
Leroy_P._Steele_Prize
airstrips & water. A first prototype was built and flown by Barcelona-based Singular Aircraft in 2015, with a second prototype flying in July 2020. Four main
Singular_SA03
American mathematician
National Academy of Sciences. Harvey, Reese; Polking, John (1970). "Removable singularities of solutions of linear partial differential equations". Acta Mathematica
F._Reese_Harvey
1985 novel by William Sleator
relationship forever. In his review of Singularity, Orson Scott Card, bestselling author of The Ender Saga, wrote "Singularity... is a masterpiece... I can't
Singularity_(Sleator_novel)
Proposed theories of gravity
additional publications in 1978 and 1980, in which he made an attempt "to remove singularities arising in general relativity by modifying it so as to take into
Bimetric_gravity
Russian-British scientist (1952–2025)
he obtained a master's degree with a thesis entitled Sets of removable singularities in Banach spaces and continuous maps under the supervision of Russian
Alexander_Gorban
Book by James D. Miller
associated with the technological singularity, including cognitive enhancement and AI. Miller, James D. (2012-10-16). Singularity Rising: Surviving and Thriving
Singularity_Rising
Singular, feminine, third-person pronoun
herself in Wiktionary, the free dictionary. In Modern English, she is a singular, feminine, third-person pronoun. In Standard Modern English, she has four
She_(pronoun)
squares is a branched covering with branch points the singularities (the cone angle at a singularity is proportional to the degree of branching). Suppose
Translation_surface
Concept in differential equation mathematics
coefficients are analytic functions, and singular points, at which some coefficient has a singularity. Then amongst singular points, an important distinction
Regular_singular_point
Conjecture in symplectic geometry
curvature flow. In particular Joyce described the types of finite-time singularity formation which are expected to occur in the Lagrangian mean curvature
Thomas–Yau_conjecture
Physical theory of the cosmos
measurements of the expansion rate of the universe place the initial singularity at an estimated 13.787±0.02 billion years ago, which is considered the
Big_Bang
1994 novel by Roger Williams
its own specialised processors, ultimately heralding a technological singularity. After remaining unpublished for years, the novel was published online
The Metamorphosis of Prime Intellect
The_Metamorphosis_of_Prime_Intellect
American mathematician
F. Reese; Lawson, H. Blaine (2013). "Existence, uniqueness and removable singularities for nonlinear partial differential equations in geometry". Surveys
H._Blaine_Lawson
American animated drama television series
well as its portrayal of the singularity. The series begins with the world on the verge of a technological singularity, spearheaded by the development
Pantheon_(TV_series)
Inequality relating to the Laplace operator
Juan; Ponce, Augusto (2003). "Variants of Kato's inequality and removable singularities". Journal d'Analyse Mathématique. 91: 143–178. doi:10.1007/BF02788785
Kato's_inequality
Coordinate system for the Schwarzschild geometry
and are well-behaved everywhere outside the physical singularity. There is no coordinate singularity at the horizon. The Kruskal–Szekeres coordinates also
Kruskal–Szekeres_coordinates
Comic book series
new character named Singularity, a pocket universe that gains self-consciousness during "Secret Wars". Wilson likened Singularity to Q from Star Trek:
A-Force
Theoretical construct in flow physics
The Prandtl–Glauert singularity is a theoretical construct in flow physics, often incorrectly used to explain vapor cones in transonic flows. It is the
Prandtl–Glauert_singularity
Topics referred to by the same term
Riemann's theorem on conformal mappings. Riemann's theorem on removable singularities. Riemann's theorem on the rearrangement of terms of a series. This
Riemann's_Theorem
Latvian-American mathematician (1914–1993)
Riemann's theorem on removable singularities, showing that any isolated singularity of a pencil of minimal surfaces can be removed; he spoke on this result
Lipman_Bers
REMOVABLE SINGULARITY
REMOVABLE SINGULARITY
Boy/Male
Hindu, Indian, Parsi
Memorable
Boy/Male
Sikh
Immovable Prince
Girl/Female
Hindu, Indian, Marathi, Tamil
Immovable
Boy/Male
Indian, Punjabi, Sikh
Memorable
Boy/Male
Indian, Telugu
Memorable Things
Girl/Female
Indian, Punjabi, Sikh
Immovable
Boy/Male
Sikh
Immovable morals
Boy/Male
Tamil
Unmovable
Boy/Male
Indian, Punjabi, Sikh
Immovable; Firm
Boy/Male
Indian, Punjabi, Sikh
Immovable Light
Boy/Male
Hindu
Immovable morals
Girl/Female
Hindu, Indian, Marathi
Immovable
Boy/Male
Hindu, Indian
The Immovable
Boy/Male
Indian, Sanskrit
Immovable; Unassailable
Boy/Male
Tamil
Dhruvav | தà¯à®°à¯à®µà®¾à®µ
The immovable
Dhruvav | தà¯à®°à¯à®µà®¾à®µ
Boy/Male
Tamil
Immovable morals
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Unmovable
Boy/Male
Sikh
Immovable
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Stable; Immovable
Boy/Male
Indian, Punjabi, Sikh
Memorable
REMOVABLE SINGULARITY
REMOVABLE SINGULARITY
Boy/Male
Muslim
Messenger
Boy/Male
Hindu
Boy/Male
Tamil
Lord Vishnu, Refuge of Man
Boy/Male
Hindu, Indian, Punjabi, Sikh
The Power of Lord Ganesha
Boy/Male
Assamese, Bengali, Indian
Pomegranate; One Type of Fruit
Girl/Female
Hindu, Indian, Tamil
A Precious Stones
Boy/Male
Sikh
Light, Lustrous, Power
Male
Finnish
Finnish form of Old Norse Þorsteinn, TORSTI means "Thor's stone."
Biblical
one that takes or possesses
Boy/Male
Muslim
Jupiter. Planet.
REMOVABLE SINGULARITY
REMOVABLE SINGULARITY
REMOVABLE SINGULARITY
REMOVABLE SINGULARITY
REMOVABLE SINGULARITY
a.
That may be removed; removable.
v. t.
A removable sliding bottom to galley.
a.
Changing from one time to another; as, movable feasts, i. e., church festivals, the date of which varies from year to year.
a.
Steadfast; fixed; unalterable; unchangeable; -- used of the mind or will; as, an immovable purpose, or a man who remain immovable.
n.
Lands and things adherent thereto by nature, as trees; by the hand of man, as buildings and their accessories; by their destination, as seeds, plants, manure, etc.; or by the objects to which they are applied, as servitudes.
n.
A false front, or removable ornamental covering.
a.
Immovable.
a.
Not liable to be removed; permanent in place or tenure; fixed; as, an immovable estate. See Immovable, n.
a.
Incapable of being moved; firmly fixed; fast; -- used of material things; as, an immovable foundatin.
a.
Capable of being moved, lifted, carried, drawn, turned, or conveyed, or in any way made to change place or posture; susceptible of motion; not fixed or stationary; as, a movable steam engine.
a.
Not amovable or removable.
a.
Admitting of being resolved; admitting separation into constituent parts, or reduction to first principles; admitting solution or explanation; as, resolvable compounds; resolvable ideas or difficulties.
a.
Capable of being revoked; as, a revocable edict or grant; a revocable covenant.
a.
Not removable; immovable; inflexible.
a.
Admitting of being removed.
n.
That which can not be moved.
a.
Removable.
a.
Reprovable.
n.
The removable cover of a journal box.
a.
Worthy to be remembered; very important or remarkable.