Silvia
Reputation
Next privilege 250 Rep.
 Oct 17 comment Expected number of people to not get shot? I'm not a mathematician, so I'm not that confident. And I think the expected number is much harder to get :) already +1 of course. Oct 17 comment Expected number of people to not get shot? Can we generalize the problem to $k$-dimension? Sep 24 awarded Autobiographer Aug 23 comment Simplify $\tan^{-1}[(\cos x - \sin x)/(\cos x + \sin x)]$ define simplest please. Jul 23 awarded Supporter Jul 3 awarded Teacher Jun 13 revised Compound Poisson process with exponential distribution added 12 characters in body Jun 13 awarded Editor Jun 13 revised Compound Poisson process with exponential distribution added 10 characters in body Jun 13 answered Compound Poisson process with exponential distribution Jul 21 revised Method for variable substitution in multiple summation added a tag Jul 21 comment Method for variable substitution in multiple summation Yes they are:( I used one of the explicit sum formulas of Chebyshev polynomial (mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html eq.15), which introduces those floor functions. Jul 21 comment Method for variable substitution in multiple summation @ Christian Blatter: Thanks very much for your answer. I understand the difficulties of counting lattice points in disk, but if considering the summation region bounded only by integer coefficients planes (like $\sum_k A_k x_k=B$ where $A_k, B\in \mathbb{Z}$), the problem might be much simpler and there might even exist a systematical technique for it. Besides, I'm thinking of using Iverson's bracket to avoid dealing with those tricky boundary conditions. Jul 21 comment Method for variable substitution in multiple summation @Patrick Da Silva: Yes I draw 2-dim or 3-dim axes too when I do the transformation by hand :D But if I have many levels of sum, this will be inefficient cause it's hard to draw high dimension, and those floor and ceiling functions and steps$\neq 1$ are bothering. I think I need to treat the whole summation region as a high dimension polyhedron and find a systematical routine to deal with it. Jul 21 awarded Student Jul 21 asked Method for variable substitution in multiple summation