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) =-si...
Find Laurent series expansion centered on z= 0 for |z|<1 and for |z|>1 f(e) f() = -1-2) 1+22
) 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
(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
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...
(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. 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)
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
find Laurent series expression of in region a- 1< |z| < 3 b- 0< |z+1| < 2 (2+1)(2+3)
2 7. Find the Laurent series of the function f(2) = in the region 1 < 121 < 2. (z+1)(2 – 2)