[Q3.] Expand f(x) = - via a Laurent series valid for 2 > 1. z(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
in a laurent series valid (z-2) (1+2) 2+11 > 2
Develop f(z)=1/(z(z-3)) in a laurent series valid for the indicated
domains.
determine the nature of the singularities of the following
functions.
0시리 <3 6) 3<시리 22 13) f(3) = -1 14) FCZ) = sen (42) - 42 Z 22
1 9. Expand f(z) = (2-1)-(2-6) as a Laurent series a) for 12-11 > R. R=? (Note: Pay attention, it is for >R, NOT <R.) b) for 12 - 41 <K. K=?
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.
) 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
2 7. Find the Laurent series of the function f(2) = in the region 1 < 121 < 2. (z+1)(2 – 2)
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...
(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}.
Solve:
Laurent series h(z) - Z O CIZ + 11 <3 (2+1)(2-2)