# point at infinity

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## 1—10 of 74 matching pages

##### 2: 23.20 Mathematical Applications
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. …
##### 3: 1.10 Functions of a Complex Variable
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
Equation (21.7.1) determines a plane algebraic curve in ${\mathbb{C}}^{2}$, which is made compact by adding its points at infinity. …
##### 5: 28.2 Definitions and Basic Properties
This equation has regular singularities at 0 and 1, both with exponents 0 and $\frac{1}{2}$, and an irregular singular point at $\infty$. …
##### 6: 2.7 Differential Equations
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). …
##### 7: 1.9 Calculus of a Complex Variable
###### §1.9(iv) Conformal Mapping
The extended complex plane, $\mathbb{C}\,\cup\,\{\infty\}$, consists of the points of the complex plane $\mathbb{C}$ together with an ideal point $\infty$ called the point at infinity. …
##### 8: 6.4 Analytic Continuation
Analytic continuation of the principal value of $E_{1}\left(z\right)$ yields a multi-valued function with branch points at $z=0$ and $z=\infty$. …
##### 9: 15.2 Definitions and Analytical Properties
As a multivalued function of $z$, $\mathbf{F}\left(a,b;c;z\right)$ is analytic everywhere except for possible branch points at $z=0$, $1$, and $\infty$. …
##### 10: 16.2 Definition and Analytic Properties
Elsewhere the generalized hypergeometric function is a multivalued function that is analytic except for possible branch points at $z=0,1$, and $\infty$. …