Branch Definition and 212 Threads

I need help with a branch cut intgration. The problem is to show the following for 0< \alpha <1: \int_{0}^{\infty}{x^{\alpha - 1} \over x+1}={\pi \over sin\alpha\pi} I used the standard keyhole contour around the real axis (taking that as the branch cut), but using the residue theorem...

I was wondering,when we have a voltage source connected to a node in series with a resistance connected to the ground like this: ,when determining the current on the branches through node method is the current on that branch 5/1k or v1+5/1k...

In complex analysis we say that for fn's like lnz we apply a branch cut along positive x-axis to make sure it's single valued. i.e restrict theta s.t 0<=theta<2Pi but we never allow theta to equal 2Pi as this would make lnz take on 2nd value. Let us integrate around a contour which goes from...

Its me again! I listend to what you said about right when the switch is closed there is a huge change in current so the inductor is going to have massive resistance, but in this case, the current still seemed to go directly into the inductor and not branch off into the 5 OHM resistor toward the...

Well, this is interesting, and shows how little Bush knows about dealing with "terrorism" The UK tried this tactic with the IRA for years, and quiet frankly it had the opposite effect than was needed. War will not beat al-queda, deplomacy is needed now, if peace is actually what is wanted...

It is rather well known that the color of flowers on Hydrangea depends upon the pH of the soil in which it is planted. Low pH in the soil means blue flowers and high pH means pink. Here is a quote from the Texas A&M site on Hydrangea: Sometimes a single plant may have shades of both pink and...

What is the relationship between the number of branch points and the number of independent current in a circuit?

Hi, I've typed up my work. Please see the attached pdf. Basically, I am trying to sovle this problem. \int_0^\infty \frac{x^\alpha}{x^2+b^2} \mathrm{d}x for 0 <\alpha < 1. I follow the procedure given in Boas pg 608 (2nd edition)...and everything seems to work. However, when I...

When disputes occur between Congress and the President, what is the tendency of the federal judiciary? For another question about the Prez, what are his constraints on foreign policy? Thanks for any help.

which is the newest field in maths? when i mean "new" i refer to minimun 25-50 years of research in the field back from when it was founded? perhaps it's category theory or are there newer?

Please answer ASAP."List the major branch of Physics and its 2 subfields we have studied and discuss each." (We have been studying Mechanics)... what are the subfields? Or am I reading the question wrong. I am so confused. *Steph*

From my dear collegues: National Geographic: http://news.nationalgeographic.com/news/2003/05/0520_030520_chimpanzees.html