GATE EC 2016 Set 3 — Question 12
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Engineering Mathematics → Complex Analysis → Residue Theorem & Contour Integration
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Question
For , the residue of the pole at is
Correct answer
1 to 1
Solution
The function is .
The pole is at .
We need to find the order of the pole.
The Taylor series expansion of around is:
So,
This is the Laurent series expansion of around .
The residue of at is the coefficient of the term in its Laurent series expansion.
From the expansion, the coefficient of is .
Thus, the residue of the pole at is .
The pole is at .
We need to find the order of the pole.
The Taylor series expansion of around is:
So,
This is the Laurent series expansion of around .
The residue of at is the coefficient of the term in its Laurent series expansion.
From the expansion, the coefficient of is .
Thus, the residue of the pole at is .
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