MHB Tricky complex analysis questions....

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The discussion focuses on combining functions with poles, specifically how to create and prove rules for operations like addition, multiplication, and division of functions f and g at a pole c. Participants suggest using the Laurent series expansion of these functions around the pole to analyze the effects of arithmetic operations on the series. Additionally, the thread addresses finding and classifying the poles of the function (cot(z) + cos(z)) / sin(2z). The classification of these poles is tied back to the rules established for combining functions at poles. Understanding these concepts is crucial for complex analysis and the behavior of functions near singularities.
Zukias
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i.
Let f and g be functions with a pole at c. Create rules (and prove them) about how we can combine f and g at c.

and ii: Find the poles of the function :
\frac{cotz+cosz}{sin2z}

and classify these poles using part i.
 
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Do you mean what happens to c when considering f+g ?
 
ZaidAlyafey said:
Do you mean what happens to c when considering f+g ?

I think it means when functions are multiplied, added, substracted, divided etc, that's what I'm assuming anyway
 
I'll say write the Laurent expansion of f and g around the pole c and see what happens when you apply the arithmetic operations on the series.
 

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