(a) Find the coefficients an and bn of the Laurent series of the function f(z) : =Z Justify all of your steps. ∞ Σan(z-zo)" + Σ bn(z-zo)-n ·Σb n=1 n=0 z¹5 sin (25) valid on the set {z € C : 0 < |z| < 10}, where zo = 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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a)

(a) Find the coefficients an and b₁ of the Laurent series
∞
Σan (z −zo)" +
An (z − zo)” + Σ bn(Z — Zo)¯n
-
n=0
n=1
of the function f(z) = z¹5 sin (25) valid on the set {z € C : 0 < |z| < 10}, where zo = 0.
Justify all of your steps.
Transcribed Image Text:(a) Find the coefficients an and b₁ of the Laurent series ∞ Σan (z −zo)" + An (z − zo)” + Σ bn(Z — Zo)¯n - n=0 n=1 of the function f(z) = z¹5 sin (25) valid on the set {z € C : 0 < |z| < 10}, where zo = 0. Justify all of your steps.
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