question 5c 5. Find the Laurent series expansion of: (a) f(x) = 2*1 about i, (b)...
(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}.
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
+ for (a)0</zl</ (6) 12/> 1. -6) Find the two Laurent series in powers of z that represent sin --
2. Find the Fourier Series of f(T). TER,(-2,2) (1) So, -2 <r<0, 2-I, 0<I<2.
please answer its urgent. develop f(z)=(z(z-3)) into a laurent serkes valid for the following domains develop g(z)= 1/((z-1)(z-2)) into a laurent series valid for the following domains develop h(z)= z/((z+1)(z-2)) into a laurent series valid for the following domains 7) 0 < 1 2 -3/ <3 6) 1८11-4/<4 9) 0시레시 10) 0<l2-2시 ) ۵ < ( 2 + ( ( 3 (2) 02 ( 2 -2) 3.
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
(1 point) Find the Fourier series expansion, i.e., f(x) [an cos(170) + by sin(t, x)] n1 J1 0< for the function f(1) = 30 < <3 <0 on - SIST ao = 1 an = cos npix bn = Thus the Fourier series can be written as f() = 1/2