In mathematics, a real-valued function f on the interval [a, b] is said to be singular if it has the following properties: f is continuous on [a, b]. (**)...

Singularity functions are a class of discontinuous functions that contain singularities, i.e., they are discontinuous at their singular points. Singularity...

the Lebesgue function, Lebesgue's singular function, the Cantor–Vitali function, the Devil's staircase, the Cantor staircase function, and the Cantor–Lebesgue...

distribution has singular support { 0 } {\displaystyle \{0\}} : it cannot accurately be expressed as a function in relation to test functions with support...

reciprocal function f ( x ) = 1 / x {\displaystyle f(x)=1/x} has a singularity at x = 0 {\displaystyle x=0} , where the value of the function is not defined...

problem fails to have a unique solution need not be singular functions. In some cases, the term singular solution is used to mean a solution at which there...

isolated singularity is one that has no other singularities close to it. In other words, a complex number z0 is an isolated singularity of a function f if...

differential equation as the singular point at 1 is moved towards the singular point at ∞, the confluent hypergeometric function can be given as a limit of...

The technological singularity—or simply the singularity—is a hypothetical point in time at which technological growth becomes completely alien to humans...

removable singularity of a holomorphic function is a point at which the function is undefined, but it is possible to redefine the function at that point...

max is not continuous at the singular set where two coordinates are equal, while the uniform limit of continuous functions is continuous. The reason it...

the Minkowski question mark function to  ?:[0,1] → [0,1], it can be used as the cumulative distribution function of a singular distribution on the unit interval...

In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a rescaling followed...

K(x,y)f(y)\,dy,} whose kernel function K : Rn×Rn → R is singular along the diagonal x = y. Specifically, the singularity is such that |K(x, y)| is of size...

Green's functions for the Klein–Gordon equation. There are related singular functions which are important in quantum field theory. These functions are most...

particularly singularity theory, the Milnor number, named after John Milnor, is an invariant of a function germ. If f is a complex-valued holomorphic function germ...

regular singularities. The cases where the solutions are algebraic functions were found by Hermann Schwarz (Schwarz's list). The hypergeometric function is...

is called singular, if it is singular with respect to the Lebesgue measure on this space. For example, the Dirac delta function is a singular measure....

F_{\rm {smooth}}} and its singular F s i n g u l a r {\displaystyle F_{\rm {singular}}} parts. The product of generalized functions F {\displaystyle F} and...

entire function will produce a harmonic function with the same singularity, so in this case the harmonic function is not determined by its singularities; however...

essential singularity of a function is a "severe" singularity near which the function exhibits striking behavior. The category essential singularity is a "left-over"...

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 (see essential...

geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter. The precise definition of a singular point depends...

distribution (with a probability mass function), an absolutely continuous distribution (with a probability density), a singular distribution (with neither), or...

coefficients are analytic functions, and singular points, at which some coefficient has a singularity. Then amongst singular points, an important distinction...

production by Santa Clara Vanguard Drum and Bugle Corps a singular function in mathematics Cantor function Baguenaudier, a disentanglement puzzle This disambiguation...

to consider that one has a multi-valued function, which is analytic everywhere except for isolated singularities, but whose value may "jump" if one follows...

cases, the value of the function at the removable singularity at zero is understood to be the limit value 1. The sinc function is then analytic everywhere...

of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for any function f : C ∖ { a k }...

"pole" (or isolated singularity) of a function is a point where the function's value becomes unbounded, or "blows up". If a function has such a pole, then...