20.6. Find the (unique) Laurent expansion of each of the following functions in each of its regions of analyticity: sinh z – z (d) 1 1 (a) (z – 2)(z – 3)* (b) z cos(z²). (c) 2²(1 – 2)" 22 – 4 z4 1 (e) (1 - 1 1 2)3* (f) 2 (h) (2² – 1)2 * 9. z – 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The question is about Taylor And Laurent Theorem.

Please solve parts g, h and i.

20.6. Find the (unique) Laurent expansion of each of the following functions
in each of its regions of analyticity:
sinh z
(d)
1
1
(a)
(z – 2)(z – 3)*
(b) z cos(2²).
(c)
2² (1 – 2)'
z4
-
1
1
(f)
4
1
(e)
(1
(g)
(h)
(2² – 1)2 *
1
(i)
- Z
Transcribed Image Text:20.6. Find the (unique) Laurent expansion of each of the following functions in each of its regions of analyticity: sinh z (d) 1 1 (a) (z – 2)(z – 3)* (b) z cos(2²). (c) 2² (1 – 2)' z4 - 1 1 (f) 4 1 (e) (1 (g) (h) (2² – 1)2 * 1 (i) - Z
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