Find Laurent series expansion centered on z= 0
for |z|<1 and for |z|>1
Find Laurent series expansion centered on z= 0 for |z|<1 and for |z|>1 f(e) f()...
Derive the Laurent series expansion for the function (a) f(z) := z^2 sin (1/(z − 1 )) on the exterior |z − 1| > 0 of the unit disk centered at 1, and for the function (b) g(z) := 1 /(z^2 + z − 2) in the annular region 1 < |z − 1| < 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
(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}.
Find the Laurent series (expressed as a sum) of the following functions: a) f(z) =-sinh(z) C' b)f(z) =-e
Find the Laurent series (expressed as a sum) of the following functions: a) f(z) =-sinh(z) C' b)f(z) =-e
9. Find the Laurent series about 0 that represents the complex function f(z)22 sin in the domain 0 < Izl < 00 0o rn i+ Answer:
9. Find the Laurent series about 0 that represents the complex function f(z)22 sin in the domain 0
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
sin ak 2. (1) Let k be a positive integer. Find the Laurent series expansion of f(x) = at z = 0 precisely (presenting a first few terms is not sufficient). (2) Find Res[f(x), 0). (3) Is the singularity of at z = O removable ? ਵ
(b) Determine the largest R such that the Laurent series of 2+1 f(z) = z 1 + (z-iT)(z+T) converges for 0< z-1|<R
(b) Determine the largest R such that the Laurent series of 2+1 f(z) = z 1 + (z-iT)(z+T) converges for 0
2. Find three different Laurent series representations (about 0) for the function 3 f(z)
2. Find three different Laurent series representations (about 0) for the function 3 f(z)