#1. Find the Maclaurin series for Z-3 f(2)= z²+z-20

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please solve number 1
#.
Find the Maclaurin series for
Z-3
f(2)=
z²+z-20
#2. Find the Laurent series for function f(z) =.
in the regions (a) 0</2/<3. (61 3</2100
(c) 04/2-3/<1.
#3. let fiz) be analytic in a domain D and het f'(zo) \0
for Zo ED. Show that if C is a sufficiently small circle
Centered at to, then
2πi
f'(Zol
#4. Find the Taylor series for the function
2-3
fiz) =
at the point 20 = 3.
2²47-20
ds
Pc f(s) - fize)
#5. Prove that the function of defined by
when z to
fiz) = {
(e²-1-2)/2²
is entive.
YN
when.
Z (Z-3i)
2=0
Transcribed Image Text:#. Find the Maclaurin series for Z-3 f(2)= z²+z-20 #2. Find the Laurent series for function f(z) =. in the regions (a) 0</2/<3. (61 3</2100 (c) 04/2-3/<1. #3. let fiz) be analytic in a domain D and het f'(zo) \0 for Zo ED. Show that if C is a sufficiently small circle Centered at to, then 2πi f'(Zol #4. Find the Taylor series for the function 2-3 fiz) = at the point 20 = 3. 2²47-20 ds Pc f(s) - fize) #5. Prove that the function of defined by when z to fiz) = { (e²-1-2)/2² is entive. YN when. Z (Z-3i) 2=0
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