Complex Analysis : Taylor and Laurent Series

Study concepts, example questions & explanations for Complex Analysis

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Example Questions

Example Question #1 : Taylor And Laurent Series

Find the Taylor Series expansion of 

Possible Answers:

Correct answer:

Explanation:

It is well known (can be shown by the definition) that that

Making the appropriate substitutions

Shifting the index of summation gives us

Example Question #2 : Taylor And Laurent Series

Find the first three terms of the Taylor Series of 

Possible Answers:

Correct answer:

Explanation:

Taylor Series expansion of the numerator and the denominator seperately gives us

 

A term by term multiplication gives us

Combining like terms 

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