Recent content by Pzi

Thanks for all the help. To sum things up I'd just like to say that I almost got it right after your first post. Unfortunately I made a very silly mistake at the very end. Which in turn led to a whole phase of contemplation and doubts. I attach that almost-correct handwritten solution just...

Why do you say so? (i+1)+(i+2)+(i+3)...+(N-2)+(N-1)+N = (N+i+1)(N-i)/2 Well the first term is E(kikj) added n(n-1) times isn't it? Hence E(kikj)=(N+1)(3N+2)/12 (for i≠j) which is not the same as previously stated by yourself E(kikj)=N(N+1)/4-(2N+1)/6. Sorry if I missed something. P.S...

I appreciate your dedication very much. Sorry for not getting back to this topic in a reasonable amount of time. So for i≠j you apparently got E(kikj) = N(N+1)/4 - (2N+1)/6. Meanwhile I got E({k_i}{k_j}) = \frac{1}{{\left( {\begin{array}{*{20}{c}} N\\ 2 \end{array}}...

This applies to natural numbers n and N where n<N. We have N balls representing numbers 1,2,...,N. We randomly choose n of those balls which happen to represent numbers {k_1},{k_2},...,{k_n}. We then define a random variable X = {k_1} + {k_2} + ... + {k_n}. What is the mean and variation of X...

Still looking for any insightful ideas!

Not really. Your idea requires powers like 1, 2, 4, 8, 16, 32... whereas we actually have 1, 2, 3, 4, 5, 6...

Hello. Does anybody happen to know a closed form of this infinitely nested radical? http://imageshack.us/a/img268/6544/radicals.jpg By any chance, maybe you even saw it somewhere? I haven't had too much success so far. At the moment I am so desperate that I'm even willing to try and...

Homework Statement There are N villages which have to be connected using one-way roads in a manner that for every two villages there exists at least one route to travel from one to another. How many different solutions are there? Homework Equations This fits pretty well not only into...

It is necessary for me to use Monte-Carlo method for this one. However I appreciate your observation about the precise value!

Homework Statement Integrate using Monte-Carlo method and evaluate absolute error. \int\limits_1^{ + \infty } {\frac{{\sqrt {\ln (x)} }}{{{x^5}}}dx} Homework Equations Everything about Monte-Carlo integration I guess. The Attempt at a Solution I = \int\limits_1^{ + \infty }...

Hi. Let's say there is a need to recreate a primitive plot like http://img27.imageshack.us/img27/6001/graz.png Surely I can Photoshop it, I can even generate it using Mathcad or such, but pictures look awkward when imported into documents... I dare to say I want them scalable and...

What exactly do you mean by "evaluation"? At s=0 your initial input involves division by zero... Well if you calculate a limit then everything is consistent.

It tells how "powerful" the zero is. Technically I'd say that for F(z)=(z-a)^n we have a zero of n-th order z=a because n-th derivative of F(z) at z=a is no longer equal to zero... This works for all finite arguments. How would you evaluate what is the order of zero z=0 for the function...

Are you familiar with zeros of higher order? If z=a is a zero of n-th order for a function 1/f(z) , then z=a is a pole of n-th order for a function f(z). Those two are related like that.

Yea, looks like it's indeed a non-elementary case here... As this is a part of some differential equations I will work around it (using convolution), but it will be ugly. Thanks for clarification!