How could I evaluate this IMPROPER integra?

Thread starter frasifrasi
Start date Nov 3, 2007

Nov 3, 2007

frasifrasi

Int from 1 to infinity of ln(X)/x^(3)

--> Any ideas on how to get started(mainly the technique)? thank you.

Physics news on Phys.org

Nov 3, 2007

Dick

Science Advisor

Homework Helper

You would first find an indefinite integral using integration by parts.

Nov 4, 2007

benjyk

Let u = ln x and dv/dx = x^-3 and use integration by parts.
And see what happens as the upper bound of the integral tends to infinity.

Thread 'Complex Numbers (Laurent Series)'

see attached.

View full post »

Thread 'Necessary criterion for expressing f(a + b)'

It's easy to see that any polynomial is function of that class. Also it seems that composition of exponent and polynomial is good as well. G_f(a, b) should be equal G_f(b, a) as the f(a+b) is symmetrical. Does anyone have information about this or at least related to it?

View full post »

Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...

View full post »