# point at infinity

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## 1—10 of 74 matching pages

##### 1: 1.13 Differential Equations

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###### Transformation of the Point at Infinity

…##### 2: 23.20 Mathematical Applications

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►The curve $C$ is made into an abelian group (Macdonald (1968, Chapter 5)) by defining the zero element $o=(0,1,0)$ as the point at infinity, the negative of $P=(x,y)$ by $-P=(x,-y)$, and generally ${P}_{1}+{P}_{2}+{P}_{3}=0$ on the curve iff the points
${P}_{1}$, ${P}_{2}$, ${P}_{3}$ are collinear.
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##### 3: 1.10 Functions of a Complex Variable

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►A function whose only singularities, other than the point at infinity, are poles is called a

*meromorphic function*. If the poles are infinite in number, then the point at infinity is called an*essential singularity*: it is the limit point of the poles. …##### 4: 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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##### 5: 28.2 Definitions and Basic Properties

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►This equation has regular singularities at 0 and 1, both with exponents 0 and $\frac{1}{2}$, and an irregular singular point at
$\mathrm{\infty}$.
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##### 6: 2.7 Differential Equations

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►To include the point at infinity in the foregoing classification scheme, we transform it into the origin by replacing $z$ in (2.7.1) with $1/z$; see Olver (1997b, pp. 153–154).
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##### 7: 1.9 Calculus of a Complex Variable

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###### §1.9(iv) Conformal Mapping

►The*extended complex plane*, $\u2102\cup \{\mathrm{\infty}\}$, consists of the points of the complex plane $\u2102$ together with an ideal point $\mathrm{\infty}$ called the*point at infinity*. …##### 8: 6.4 Analytic Continuation

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►Analytic continuation of the principal value of ${E}_{1}\left(z\right)$ yields a multi-valued function with branch points at
$z=0$ and $z=\mathrm{\infty}$.
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##### 9: 15.2 Definitions and Analytical Properties

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►As a multivalued function of $z$, $\mathbf{F}(a,b;c;z)$ is analytic everywhere except for possible branch points at
$z=0$, $1$, and $\mathrm{\infty}$.
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##### 10: 16.2 Definition and Analytic Properties

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►Elsewhere the generalized hypergeometric function is a multivalued function that is analytic except for possible branch points at
$z=0,1$, and $\mathrm{\infty}$.
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