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(C)!!!!! 5. Find the Laurent series expansion of: 1 (a) f(x) = 1 about i, (b)...
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}.
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
2 7. Find the Laurent series of the function f(2) = in the region 1 < 121 < 2. (z+1)(2 – 2)
) 1. Find the Laurent series of f(z) on the indicated domain. (a) -,2, on 0 < |z-i| < 2. 1+22 222z 5 , on z 1| > 1
Q3: 5 marks (A) Expand f(z) (2-1)(2-3) in a Laurent series valid for (i) Iz - 11 < 2, and (ii) Iz - 31 < 2. 1.5 marks each part (B) Use Laurent series to find the residue of f(2)= e (x - 2)-2 at its pole z = 2. 2 marks
find fourier series of Question 3 Find Fourier series of f(x)= 0 if -55x<0 and f(x) = 1 if 0<x<5 which f(x) is defined on (-5,5).
+ for (a)0</zl</ (6) 12/> 1. -6) Find the two Laurent series in powers of z that represent sin --
(a) Find the Fourier series for f(x) = -x, -1<x<1 f(x+2) = f(x)
Solve: Laurent series h(z) - Z O CIZ + 11 <3 (2+1)(2-2)
2. Find the value of c so that the function is continuous everywhere. f(x) = 02 – 22 r<2 1+c => 2 {