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...
4 KB (567 words) - 14:43, 22 January 2024
Look up Singularity or singularity in Wiktionary, the free dictionary. Singularity or singular point may refer to: Mathematical singularity, a point at...
6 KB (751 words) - 07:02, 21 August 2024
derivative, not to the original function. A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame, which...
14 KB (2,054 words) - 20:13, 21 September 2023
essential singularity of a function is a "severe" singularity near which the function exhibits striking behavior. The category essential singularity is a "left-over"...
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rigid that their isolated singularities can be completely classified. A holomorphic function's singularity is either not really a singularity at all, i.e....
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The residue of a meromorphic function f {\displaystyle f} at an isolated singularity a {\displaystyle a} , often denoted Res ( f , a ) {\displaystyle...
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mathematical singularity as a value at which a function is not defined. For that, see for example isolated singularity, essential singularity, removable...
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Residue theorem (section Removable singularities)
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...
13 KB (3,282 words) - 19:47, 28 June 2024
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...
18 KB (2,517 words) - 14:08, 22 April 2024
a Du Val singularity, also called simple surface singularity, Kleinian singularity, or rational double point, is an isolated singularity of a complex...
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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...
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{\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...
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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...
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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...
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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...
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primitive Cauchy's integral formula Winding number Laurent series Isolated singularity Residue theorem Argument principle Conformal map Schwarz lemma Harmonic...
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primitive Cauchy's integral formula Winding number Laurent series Isolated singularity Residue theorem Argument principle Conformal map Schwarz lemma Harmonic...
10 KB (1,635 words) - 21:31, 20 December 2022
Harmonic function (section Removal of singularities)
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...
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primitive Cauchy's integral formula Winding number Laurent series Isolated singularity Residue theorem Argument principle Conformal map Schwarz lemma Harmonic...
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{\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...
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punctured neighborhood of z = 0. Hence it is an isolated singularity, as well as being an essential singularity. Using a change of variable to polar coordinates...
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primitive Cauchy's integral formula Winding number Laurent series Isolated singularity Residue theorem Argument principle Conformal map Schwarz lemma Harmonic...
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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),...
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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...
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(complex analysis) Residue (complex analysis) Isolated singularity Removable singularity Essential singularity Branch point Principal branch Weierstrass–Casorati...
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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...
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a meromorphic function (defined to mean holomorphic except at certain isolated poles), resembles a rational fraction ("part") of entire functions in a...
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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...
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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...
9 KB (1,616 words) - 16:46, 22 June 2024
primitive Cauchy's integral formula Winding number Laurent series Isolated singularity Residue theorem Argument principle Conformal map Schwarz lemma Harmonic...
9 KB (1,406 words) - 23:49, 29 April 2024