# points in complex plane

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## 1—10 of 51 matching pages

##### 1: 1.9 Calculus of a Complex Variable

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►Also, the union of $S$ and its limit points is the

*closure*of $S$. … ► … ► … ►###### Jordan Curve Theorem

… ►###### §1.9(iv) Conformal Mapping

…##### 2: Bibliography D

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Uniform asymptotic solutions of second-order linear differential equations having a simple pole and a coalescing turning point in the complex plane.
SIAM J. Math. Anal. 25 (2), pp. 322–353.
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##### 3: 1.6 Vectors and Vector-Valued Functions

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►Note: The terminology

*open*and*closed sets*and*boundary points*in the $(x,y)$ plane that is used in this subsection and §1.6(v) is analogous to that introduced for the complex plane in §1.9(ii). …##### 4: 28.7 Analytic Continuation of Eigenvalues

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►As functions of $q$, ${a}_{n}\left(q\right)$ and ${b}_{n}\left(q\right)$ can be continued analytically in the complex
$q$-plane.
…The number of branch points is infinite, but countable, and there are no finite limit points.
In consequence, the functions can be defined uniquely by introducing suitable cuts in the $q$-plane.
…The branch points are called the

*exceptional values*, and the other points*normal values*. … ► …##### 5: 8.13 Zeros

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►When $x>{x}_{n}^{\ast}$ a pair of conjugate trajectories emanate from the point
$a={a}_{n}^{\ast}$
in the complex
$a$-plane.
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##### 6: 3.8 Nonlinear Equations

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►for solving fixed-point problems (3.8.2) cannot always be predicted, especially in the complex plane.
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##### 7: 1.14 Integral Transforms

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►If the integral converges, then it converges uniformly in any compact domain in the complex
$s$-plane not containing any point of the interval $(-\mathrm{\infty},0]$.
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##### 8: 21.7 Riemann Surfaces

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►Equation (21.7.1) determines a plane algebraic curve in
${\u2102}^{2}$, which is made compact by adding its points at infinity.
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##### 9: 4.3 Graphics

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►Figure 4.3.2 illustrates the conformal mapping of the strip $$ onto the whole $w$-plane cut along the negative real axis, where $w={\mathrm{e}}^{z}$ and $z=\mathrm{ln}w$ (principal value).
Corresponding points share the same letters, with bars signifying complex conjugates.
Lines parallel to the real axis in the $z$-plane map onto rays in the $w$-plane, and lines parallel to the imaginary axis in the $z$-plane map onto circles centered at the origin in the $w$-plane.
In the labeling of corresponding points
$r$ is a real parameter that can lie anywhere in the interval $(0,\mathrm{\infty})$.
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