mathematics, an 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...

Look up Singularity or singularity in Wiktionary, the free dictionary. Singularity or singular point may refer to: Mathematical singularity, a point at...

derivative, not to the original function. A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame, which...

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

The residue of a meromorphic function f {\displaystyle f} at an isolated singularity a {\displaystyle a} , often denoted Res ⁡ ( f , a ) {\displaystyle...

a Du Val singularity, also called simple surface singularity, Kleinian singularity, or rational double point, is an isolated singularity of a complex...

rigid that their isolated singularities can be completely classified. A holomorphic function's singularity is either not really a singularity at all, i.e....

mathematical singularity as a value at which a function is not defined. For that, see for example isolated singularity, essential singularity, removable...

as we desire it can be made to contain only the singularity of c due to nature of isolated singularities. This may be used for calculation in cases where...

concept as Singularity JNode, an OS similar in concept to Singularity, but with Java instead of C# with CIL JX, a Java OS that, like Singularity, uses type...

is applicable (see methods of contour integration). A "pole" (or isolated singularity) of a function is a point where the function's value becomes unbounded...

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...

{\displaystyle f(x)} for all complex numbers x {\displaystyle x} except at the singularity x = 0 {\displaystyle x=0} . The graph opposite shows e − 1 / x 2 {\displaystyle...

its Taylor series of order 1. So just having a polynomial expansion at singular points is not enough, and the Taylor series must also converge to the function...

a meromorphic function (defined to mean holomorphic except at certain isolated poles), resembles a rational fraction ("part") of entire functions in a...

primitive Cauchy's integral formula Winding number Laurent series Isolated singularity Residue theorem Argument principle Conformal map Schwarz lemma Harmonic...

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...

{\displaystyle z=0} is an accumulation point of poles and is thus not an isolated singularity. The function f ( z ) = sin ⁡ 1 z {\displaystyle f(z)=\sin {\frac...

primitive Cauchy's integral formula Winding number Laurent series Isolated singularity Residue theorem Argument principle Conformal map Schwarz lemma Harmonic...

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...

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),...

primitive Cauchy's integral formula Winding number Laurent series Isolated singularity Residue theorem Argument principle Conformal map Schwarz lemma Harmonic...

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...

primitive Cauchy's integral formula Winding number Laurent series Isolated singularity Residue theorem Argument principle Conformal map Schwarz lemma Harmonic...

a singularity on an integral interval is avoided by limiting the integral interval to the non singular domain. Depending on the type of singularity in...

it 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...

(complex analysis) Residue (complex analysis) Isolated singularity Removable singularity Essential singularity Branch point Principal branch Weierstrass–Casorati...

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...

primitive Cauchy's integral formula Winding number Laurent series Isolated singularity Residue theorem Argument principle Conformal map Schwarz lemma Harmonic...

univalent. If the limit function is non-zero, then its zeros have to be isolated. Zeros with multiplicities can be counted by the winding number 1 2 π i...