Laurent series expansion

Does the principal branch square root of z have a Laurent series expansion in the domain C{0}? Explain.

Laurent series for a trig function

Find the Laurent series for (z^2)*cos(1/(3z)) in |z| > 0

Function description in detail

Aloha, Please describe in detail the process of solving the problem. I have the answers already, I want to know HOW one arrives at the solutions. f(t) = 10,000 / 10 + 50e ^-0.5t HOW do I obtain the derivative? What is the "e" portion of the problem? I know the derivative = 250,000e^-0.5t/ (10+50e ^-0.5t)^2 Please describe in detail the steps taken to arrive at this answer. For example, Why is the top of the equation 250,000e^-0.5t? Why is the bottom (10+50e^-0.5t)^2? Where does the ^2 on the bottom come from? ------------- Please describe in detail, when t = 0, 1, 2, 3, 4,...20 for the solution of f(t). I already know the answers t=0, f(t) = 166.67 t=1, f(t) = 24... click for more

Laurent series for a complex-valued function

Consider f(z) = [(z-i)(z+4)(z-3)]^(-1) restricted to the domain of definition 0 < |z|< infinity How many different Laurent series centered at z_0 = 0 does it have? Explain. Discuss the convergence and divergence sets of each of those Laurent series. Find two non-zero terms of the Laurent series which represents this f for all z outside some circle |z| = R but diverges inside the circle and find the numerical value of R. Is this function f(z) analytic at 0? at infinity? Explain.

Poles & Singularities

Classify the behavior at infinity (analytic, pole, zero, or essential singularity; if a zero or pole, give its order) of the following functions: f1(z) = (z^3 + i)/z f2(z) = e^(tan(1/z))