Expand the given function in a Taylor series centered at the indicated point zo. Give the radius of convergence R. 1 f(z) = , Zo = 2i 3-Z %3D z- 2i + (z- 2)2 + 1 3- 2i (3 – 2)2 (3 – 21)3 R=V13 (z- 21)2 + 1 z-2i + (3 – 21)2 (3– 2)? + 3-2i R=/8 1 (z- 2)2, (z-21² | + 3-2i (2 + (2 ... 213

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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QUESTION 17
Expand the given function in a Taylor series centered at the indicated point zo.
Give the radius of convergence R.
1
f(z) =
Zo = 2i
3-z
z-2i
+
(z- 21)2
1
+
3- 2i (3 – 21)²
(3 – 21)3
R=/13
z-2i
+
(z– 21)2
+
1
3- 2i
(3 – 21)?
(3 – 2)2
R=/8
%3D
(z- 2)2
(z- 21)2
+
1
+
..
3- 2i
(3 – 21)2
(3 – 21)3
R=V11
(z– 21)2
(3 – 21)2
(z– 2)3
(3 – 21)3
1
3- 2i
R=/13
Transcribed Image Text:QUESTION 17 Expand the given function in a Taylor series centered at the indicated point zo. Give the radius of convergence R. 1 f(z) = Zo = 2i 3-z z-2i + (z- 21)2 1 + 3- 2i (3 – 21)² (3 – 21)3 R=/13 z-2i + (z– 21)2 + 1 3- 2i (3 – 21)? (3 – 2)2 R=/8 %3D (z- 2)2 (z- 21)2 + 1 + .. 3- 2i (3 – 21)2 (3 – 21)3 R=V11 (z– 21)2 (3 – 21)2 (z– 2)3 (3 – 21)3 1 3- 2i R=/13
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