regular at infinity

When the function w of one complex variable is regular in the annulus


it has a Laurent expansion

w(z)=n=-cnzn. (1)

If especially the coefficients c1,c2, vanish, then we have


Using the inversionPlanetmathPlanetmathz=1ζ,  we see that the function


is regular in the disc  |ζ|<ϱ.  Accordingly we can define that the function w is regular at infinity also.

For example,  w(z):=1z  is regular at the point  z=  and  w()=0.  Similarly, e1z is regular at and has there the value 1.

Title regular at infinity
Canonical name RegularAtInfinity
Date of creation 2013-03-22 17:37:30
Last modified on 2013-03-22 17:37:30
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 8
Author pahio (2872)
Entry type Definition
Classification msc 30D20
Classification msc 32A10
Synonym analytic at infinity
Related topic RegularFunction
Related topic ClosedComplexPlane
Related topic VanishAtInfinity
Related topic ResidueAtInfinity