Recent content by daoshay

I've got \frac{1}{e^\frac{i\pi}{8}2i} as one residue and \frac{1}{e^\frac{3i\pi}{8}(-2i)} As the other. Any encouragement to continue or abandon ship? I'll be going to my professors last office hours with this stuff, so I'll find out one way or another. Thanks...

Homework Statement I'm finding the residues of the branch cut of \int^\infty_0 \frac{dx}{x^{1/4}(x^2+1)}dx Homework Equations The Attempt at a Solution I am trying to find the residue of i I am not sure how to handle lim z->i of \frac{1}{z^\frac{1}{4}(z+i)} Any nudges...

Thanks, Halls. I realized as soon as Vela pointed that out that I shouldn't have reciprocated because of the factorials. Only the z value is reciprocated. I'd been staring at this stuff for a while and wasn't thinking clearly. You guys have been a great help.

Thanks count. Will I end up getting -f(1), f(1/1)? I haven't tried it, but based on this problem and the behavior of the essential singularity times the analytic function, that's what I'm guessing I'll get. I -will- try it later this week.

So, I've got -sin(1) and sin(1) as the residues? That feels awkward, only because none of the examples we did had residues like that. But I suppose those are numbers too.

So, I've got: \frac {1}{z}\left(1-\frac{1}{3!}+\frac{1}{5!}-\frac{1}{7!}+\cdots\right) where the alternating series is my residue and that has a limit of... (I don't recognize this one except for the coefficients in sin(x))

Thanks, Vela. For now, I'm okay with the residue of 1 being -sin(1). I'm really uncertain about how to handle the 0 singularity. Do you suggest I expand the function into the Laurent series and find the -1 coefficient? If so, do I need to substitute \frac{e^{i1/z}-e^{-i1/z}}{2i}...

Homework Statement Classify the isolated singularities and find the residues \frac {\sin(\frac {1}{z})}{1-z} Homework Equations I know the Taylor series expansion for 1/(1-z) when |z|<1 and I think I know the Taylor series for sin(1/z). The reciprocal of each term of the Taylor series of...

Now that I've got the infinite sum, should I write it out as the difference of two summations? Or is it typically acceptable to write it out as the sum of terms with a clear pattern? I will go and ask my professor about his preferred notation anyhow.

I think I've got it. Sum from n=3 -> infinity of 2^n/z^(n+4) - Sum from n=3 -> infinity of 2^(3n+2)/z^(3n+6) because when I multiply and combine terms I get 2^3/z^7+2^4/z^8+2^6/z^10+2^7/z^11+... I'm sorry about my format, latex is too smart for me.

When you say multiply out and collect terms, do you mean I need to write it out as: 8(z+2)/z^8 + 8^2(z+2)/z^11 + ... (tried to type it in latex, but it calculated it back to f(z)... impressive!) and that is the Laurent series?

Homework Statement find the Laurent series for \frac{z+2}{z^{5}-8z^{2}} in 2<|z|<\infty Homework Equations The Attempt at a Solution Well, I factored out z^{5} in the denominator, which left me with a geometric sum (since |z|>2). I've come up with...

I'm sorry, I was rushed while typing that up and I'm afraid I wasn't clear. I found the MLE for the parameter theta. I am supposed to test it for all theta for bias and then find the MSE of theta-hat. Based on the gamma family, the mean of this distribution should be 4theta --> theta =...

I have given some serious effort to working out and understanding the MLE of a distribution. From the distribution f(x;\theta)= x^{3}e^{-x/\theta}/(6\theta^{4}), I have gotten the MLE theta-hat = xbar/4 I have a lot of difficulty figuring out if it is an unbiased estimator or not. How do I...