removable%20singularity
(0.002 seconds)
1—10 of 196 matching pages
1: 1.10 Functions of a Complex Variable
…
►This singularity is removable if for all , and in this case the Laurent series becomes the Taylor series.
…Lastly, if for infinitely many negative , then is an isolated essential singularity.
…
►
►An isolated singularity
is always removable when exists, for example at .
…
►A cut domain is one from which the points on finitely many nonintersecting simple contours (§1.9(iii)) have been removed.
…
2: 25.11 Hurwitz Zeta Function
…
►
has a meromorphic continuation in the -plane, its only singularity in being a simple pole at with residue .
…
►
…
►
25.11.30
, ,
…
►
…
3: 1.4 Calculus of One Variable
4: 31.13 Asymptotic Approximations
…
►For asymptotic approximations of the solutions of Heun’s equation (31.2.1) when two singularities are close together, see Lay and Slavyanov (1999).
►For asymptotic approximations of the solutions of confluent forms of Heun’s equation in the neighborhood of irregular singularities, see Komarov et al. (1976), Ronveaux (1995, Parts B,C,D,E), Bogush and Otchik (1997), Slavyanov and Veshev (1997), and Lay et al. (1998).
5: 8.12 Uniform Asymptotic Expansions for Large Parameter
…
►The right-hand sides of equations (8.12.9), (8.12.10) have removable singularities at , and the Maclaurin series expansion of is given by
…
►A different type of uniform expansion with coefficients that do not possess a removable singularity at is given by
…
6: 20 Theta Functions
Chapter 20 Theta Functions
…7: Viewing DLMF Interactive 3D Graphics
…
►Any installed VRML or X3D browser should be removed before installing a new one.
…
8: 5.11 Asymptotic Expansions
9: 21.7 Riemann Surfaces
…
►This compact curve may have singular points, that is, points at which the gradient of vanishes.
Removing the singularities of this curve gives rise to a two-dimensional connected manifold with a complex-analytic structure, that is, a Riemann
surface. All compact Riemann surfaces can be obtained this
way.
…
►On this surface, we choose
cycles (that is, closed oriented curves, each with at most a finite number of singular points) , , , such that their intersection indices satisfy
…
►Thus the differentials , have no singularities on .
…