Recent content by Meggle

Yes, sorry, the exponent in the denominator is supposed to be 2. I was trying to show using a=z/2!+z^2/3!+... in the last two lines, i.e. the first line was for z/2!, the second line was for z^2/3!... :rolleyes: So what I have is: \frac{1}{(e^{z}-1)^{2}} = \frac{(1 - 2(\frac{z}{2!}) +...

Laurent series "throwing away" terms Homework Statement Veeeery similar to https://www.physicsforums.com/showthread.php?p=1868354#post1868354": Determine the Laurent series and residue for f(z) = \frac{1}{(e^{z} - 1)^{z}} Homework Equations We know that the Taylor series expansion...

:bugeye: O yes, I can't use Cauchy because there's more than one singular point. Cheers.

Cauchy Intergral Formula sin(i)?? Homework Statement Circle of radius 2 centered at the origin oriented anticlockwise. Evaluate: \int\frac{sin(z)}{z^{2} +1}Homework Equations I think I'm supposed to be using the Cauchy Integral Formula, so \int\frac{f(z) dz}{z - z_{0}} = 2\piif(z_{0})The...

Homework Statement For each of the following choices of f(z) use the definition of a limit to obtain lim z-->0 f(z) or prove that the limit doesn't exist (a) \frac{|z|^{2}}{z}Homework Equations Formal limit definitionThe Attempt at a Solution f(z) = \frac{|z|^{2}}{z} f(z) = \frac{x^{2} +...

Homework Statement Scanned and attached Homework Equations I am guessing a combination of induction and the telescoping property. The Attempt at a Solution I'm studying this extramurally, and I've just hit a wall with this last chunk of the sequences section, so if someone can...

Directly as in the same way as below (i.e. without my + becoming a -), or by calculating the s3 and s2 explicitly, or some other way?

Oh yeah. Ack! I've been doing my head in over a typo! :blushing: Thanks.

Homework Statement I'm looking for a kick in the right direction of how to approach it from 1b onwards ('cos thankfully I can figure out 1a for myself). Please see the attached screenshot (I'm not good at making the formulas appear right). Homework Equations I'm really not sure. I've noticed...

Hang on, so that's actually the solution? \epsilon_{ijk}\epsilon_{jmn}\epsilon_{nkp} = \epsilon_{imp} OoooOooo. I was on the wrong track! Yeepers. Thanks for all your help! :cool: (I'll be minding out for that sword now...)

Ummmmerrrrrr: \epsilon_{ijk}S_{ij} = \epsilon_{123}S_{12} + \epsilon_{312}S_{31} + \epsilon_{231}S_{23} + \epsilon_{321}S_{32} + \epsilon_{213}S_{21}+ \epsilon_{132}S_{13} \epsilon_{ijk}S_{ij} = (1)S_{12} + (1)S_{31} + (1)S_{23} + (-1)S_{32} + (-1)S_{21} + (-1)S_{13} \epsilon_{ijk}S_{ij}...

Soooooo, instead of what I had done: (\deltakm \deltain - \deltakn\deltaim)\epsilonnkp = \deltakm \deltain\epsilonnkp - \deltakn\deltaim\epsilonnkp \deltakm \deltain \epsilonnkp - \deltakn\deltaim \epsilonnkp = \epsilonimp - \deltaim\epsilonnnp That looks like I've done something wrong...

Oh! Ok, thanks! Now if I assign all the possible values to i, m, and p, I think I end up with 0 still? εimp = ε123 + ε231... εimp = 1 + 1 + 1 - 1 - 1 - 1 + (a whole bunch of zeros where i = m etc) εimp = 0 Sorry, I know this point should be really obvious. My course readings seem to...

I can't prove that. It's stated without proof in my course readings and I haven't managed to figure it out. I don't know how to operate the Levi-Civita tensor either (yes, I'm in trouble, I know). So is this a way to answer the whole question? And what I had done isn't right at all?

Homework Statement Show that \epsilon_{ijk}a_{ij} = 0 for all k if and only if a_{ij} is symmetric.Homework Equations The Attempt at a Solution The first bit I think is just like the proof that a symmetric tensor multiplied by an antisymmetric tensor is always equal to zero. \epsilon_{ijk} = -...