GATE 2021 MA – Question 57
On |z|<2π, f(z)=3z²/(1−cos z) for z≠0 and f(0)=6. If f=Σₙ₌₀∞a_nzⁿ, find 6a₂.
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Show answer and explanation
Correct answer: 3 to 3
Explanation
Use 1−cos z=(z²/2)(1−z²/12+O(z⁴)). Thus f=6/(1−z²/12+O(z⁴))=6+z²/2+O(z⁴). Therefore a₂=1/2 and **6a₂=3**.