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1: 1.13 Differential Equations
Transformation of the Point at Infinity
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 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 1 2 , and an irregular singular point at . …
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, { } , consists of the points of the complex plane together with an ideal point called the point at infinity. …
8: 6.4 Analytic Continuation
Analytic continuation of the principal value of E 1 ( z ) yields a multi-valued function with branch points at z = 0 and z = . …
9: 15.2 Definitions and Analytical Properties
As a multivalued function of z , 𝐅 ( a , b ; c ; z ) is analytic everywhere except for possible branch points at z = 0 , 1 , and . …
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 . …