5. Define the function 22 f(x) = 22 +1 For each annulus region given below, find...
Complex Analysis:
= Define the function 22 f(z) 22 +1 For each annulus region given below, find the Laurent series of f(z) convergent in the region. (a) 0 < 12 – il < 2 (b) 1 < 121.
complex anaylsis
f(2)= 22 2z 2²+1 For each annulus region below, find the Laurent series of fiz) convergent convergent in the region (i) OC/Z-il<2 12IZI
(C)!!!!!
5. Find the Laurent series expansion of: 1 (a) f(x) = 1 about i, (b) f(x) = 22 + atz, convergent on {2< 121 < 4}, (c)* f(x) = 273-33+2, convergent on {{ < \z – 11 <1}.
2 7. Find the Laurent series of the function f(2) = in the region 1 < 121 < 2. (z+1)(2 – 2)
question 5c
5. Find the Laurent series expansion of: (a) f(x) = 2*1 about i, (b) f(x) = 22 + 1-2, convergent on {2 < 121 <4}, (c)* f(x) = 2,2-33+2, convergent on {j < lz - 11 < 1}.
Find the Taylor series of f(x) and determine the radius of convergence 1 f(z) center: 1+ i 1+2z Expand the function f(z) in the Laurent series and determine the region of convergence f(z)= 1+z center: z -i Find all Taylor and Laurent series and determine the region of convergence. f() center: z1
Find the Taylor series of f(x) and determine the radius of convergence 1 f(z) center: 1+ i 1+2z Expand the function f(z) in the Laurent series and determine...
Question one (9 marks total, 3 marks each) Let f(2)= Z 22-32+2 a. Find a Maclaurin series for f(z) in the region [z] < 1. b. Find a Laurent series for $(2) in the region 1 < lz[< 2. c. Find a Laurent series for S(z) in the region [2] > 2. Om01
Given that f(x) = Vx+ 3 – 5 -, define the function f(x) at 22 so that it becomes continuous at 22. X – 22 a) Of(22) = 10 b) O Not possible because there is an infinite discontinuity at the given point. c) Of(22) = 0 1 d) Of(22) = 10 e) Of(22) = 3
A)
B)
C)
1 Find the Laurent series for 22 +22 for 0 < 121 < 2 Find the Laurent series for (z+2)}(3-2) for 2 – 3) > 5 1 Find the Laurent series for z2(z-i) for 1 < 12 – 11 < V2
Do Task 212
Task 211 (C). Find the Laurent series of exp z exp-, and exp-2 at zo = 0. From the definition of the coefficients for the Laurent series off at zo, we see that a-1 = Res(f, zo). Sometimes it is easier to find the Laurent series than the residue directly Task 212 (C). Using the results of Task 211, find Res (exp 1,0), Res(-exp z,0), and Res(exp "In fact, given a function f(z) that is holomorphic on...