3. Calculate the Laurent series for 526 when k-2 2. Hint: This is VERY tricky. Be...
Laurent series
the
following function open the Laurent series in 1<|z+1|<3
1. Aşagıdaki fonksiyonu 1 <1: +11 < 3 bölgesinde Laurent SC 223-2)
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
Solve:
Laurent series h(z) - Z O CIZ + 11 <3 (2+1)(2-2)
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
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)
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
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...
2 7. Find the Laurent series of the function f(2) = in the region 1 < 121 < 2. (z+1)(2 – 2)
find Laurent series expression of
in region
a- 1< |z| < 3
b- 0< |z+1| < 2
(2+1)(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