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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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
Transcribed Image Text:Please answer #10 and #15 only
Find the center and the radius of convergence.
η
(−1)
(2η)!
6. Σ 4(z + 1)"
Σ
n=0
∞
10. Σ
n=0
8. Σ (z – πί)"
n!
n=0
12. Σ
n=0
14. Σ
n=0
16. Σ
n=0
n
η
(z - 2i)n
2.
n
η
(−1)"n
gn
1
5.
2+z4
7. cos2 ez
4. Σ
n=0
(-1)"
22n(n!)2 +
(3η)!
2¹ (n!)³ 2
η
2η
των
- 1²
2 εκα(4*) ar
Γ
9.
exp
dt
2
Σ(3)
3. Στη
1
(z + i)2n
n=0
η
η
3(1 – i)"
n!
n
5. Σ (") (4₂
n=2
9. Σ
n=0
11.
(4z + 2i)n
7. Σ
n=0
15. Σ
Σ(
n=0
(z – i)
n(n − 1)
3η
n=0
17. Σ
n=1
4n
13. Σ 16"(z + i)tn
n=0
Please answer #9 only
Find the Maclaurin series and its radius of convergence.
3. sin 2,2
z + 2
2- i
1 + 5i
2n
n(n + 1)
(2η)!
4" (n!) ² (z - 2i)n
4.
(z – i)2η
6.
η
1
_2n+1
Z
Please answer #5 only
Where does the power series converge uniformly? Give
reason.
2
Z
1
1 + 3iz
TT
8. sin2 =
10. exp (23)| exp (−12) dt
2η
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