M417
Fall 1996
hw7.tex due October 21, 1996
Using anything that you know, including known Taylor series expansions, find the indicated Taylor series and the radius of convergence.
1.
e
z
= ∑
n=0
∞
a
n
(z−a)
n
, |z−a| < ?.
2.
sin(z) = ∑
n=0
∞
a
n
(z−\dfracπ2)
n
, |z−\dfracπ2| < ?
3.
z
3
+ 4 z
2
+ 10z −8 = ∑
n=0
∞
a
n
z
n
, |z| < ?
4.
z
3
+ 4 z
2
+ 10z −8 = ∑
n=0
∞
a
n
(z−3)
n
, |z−3| < ?
5.
\dfrac11 +z
2
= ∑
n=0
∞
a
n
(z−3)
n
, |z−3| < ?
Hint: \dfrac11 +z
2
= \dfrac12i{ \dfrac1z−i−\dfrac1z+i}
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On 06 Feb 2017, 13:19.