Question

Please find the Laurent Series of z/(z-1)(z-3), and determine its type of isolated singular point(removable, pole(s), essential)

Answer #1

the expansions are Laurent series expansion as you can see..

Complex analysis
For the function f(z)=1/[z^2(3-z)], find all possible Laurent
expansions centered at z=0.
then find one or more Laurent expansions centered at z=1.

In the next two problems, find all Laurent series around the
indicated point and state the regions of convergence.and Find the
value of the 3rd term evaluated at ? = 2
3)?(?) = sin 1 /? , ?0 = 0 4) ?(?) = 1/ ? , ?0 = 3i

Find at least one solution about the singular point x = 0 using
the power series method. Determine the second solution using the
method of reduction of order.
xy′′ + (1−x)y′ − y = 0

1.
Determine
whether the series is convergent or divergent.
a)
If
it is convergent, find its sum. (using only one of the THREE:
telescoping, geometric series, test for divergence)
summation from n=0 to infinity of
[2^(n-1)+(-1)^n]/[3^(n-1)]
b) Using ONLY
the
Integral Test.
summation from n=1 to infinity of
n/(e^(n/3))
Please give
detailed answer.

Find the point(s) of intersection, if any, of the line
x-2/1 = y+1/-2 = z+3/-5 and the plane 3x + 19y - 7a - 8 =0

1/2z+3 expand into taylor series at z = -2 and find radius of
convergence

G(s) = K/(s+3)2
Determine the System Type
(Step, Ramp, Parabola) and find the steady state error

Find the distance from the point P(3,5,6) to the line (x-1)/2 =
(y+1)/3 = (z-1)/3

Find a power series expansion for the following function, and
determine its radius of con-
vergence. Please Show ALL steps
f(x) = x^2 arctan(3x)

Find the minimal distance from the point P = (-3, -1, 0) to the
surface z = sqr roo(1− 4x − 4y)

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