Understanding and Calculating Residues for 1/(1+z²+z⁴)

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Homework Help Overview

The discussion revolves around calculating the residue of the function 1/(1+z²+z⁴) within the context of complex analysis. Participants are exploring the concept of residues and their significance in relation to singularities of the function.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to define what a residue is and how it relates to singularities. Questions are raised about whether residues are simply the discontinuities of the function and how to calculate them accurately.

Discussion Status

The discussion is ongoing, with participants providing insights into the definition of residues. Some suggest that the residue is related to the coefficient of a series expansion at the singularity, while others question whether the original poster's textbook provides a clear definition.

Contextual Notes

There appears to be some uncertainty regarding the definition of residues and their calculation, as well as potential reliance on external resources such as textbooks for clarification.

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Homework Statement



computing the residue;
1/(1+z²+z⁴)

Homework Equations



Can someone explain to me what a residue is and how to calculate it! Is it simply the discontinuities of the function?

The Attempt at a Solution

 
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Its the co-efficient of the series expansion term at the singularity I think.
 


Doesn't your complex analysis text define it? :confused:
 


Gregg said:
Its the co-efficient of the series expansion term at the singularity I think.
The residue is the coefficient of (x- x0)-1 in a series expansion about the pole.
 

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