(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...
exercise 4 please 1. Expand the function in a Laurent series that converges for 0 < [z] <R and determine the precise region of convergence. Show details. a. zz-1) (10%) 72-73 (10%) ez b. 2. Determine the location and order of the zeros. a. sin 2 (10%) b. coshºz (10%) 3. Residue integration a. Dedz,c: [2] = a (15%) b. $ 273dz,c: [2] => (15%) 4. Evaluate the following integrals. Show details. a. Lorem (15%) b. Lo**ay (15%)
) 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
Find Laurent series expansion centered on z= 0 for |z|<1 and for |z|>1 f(e) f() = -1-2) 1+22
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...
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=?
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
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
find Laurent series expression of in region a- 1< |z| < 3 b- 0< |z+1| < 2 (2+1)(2+3)
= t a r has a Laurent series representation about the 2. Show that f(s) = point = = i given by ř (1 - i)n-1 f(3) = (valid for 12-il > 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)