Singularity at infinity and residue at infinity.
Singularity at infinity and residue at infinity for a complex function of a complex variable.
Chapters:
00:00 Introduction
02:04 point at infinity and classification
07:40 exercises point at infinity
18:09 residue at infinity and calculation of an integral
In the previous lessons we have dealt with the topic of isolated singular points by identifying the essential singularities, the poles and the eliminable singularities.
Furthermore, we are able to determine the residue of the function in the aforementioned isolated singular points, both by using the theorems and by proceeding with the Laurent series development.
With this lesson, we will take a step forward by classifying the point at infinity of a holomorphic function. The considerations are similar to those discussed for the finite points of the complex plane.
The concept of residue of a function at infinity is very useful in order to deal with integrals with the residue method.
Isolated singular points and residue of a function
• Punti singolari : polo , singolarità fitti...
Residue theorem and solution of an integral
• Integrali con il teorema dei residui .
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