Recent content by photis

Well, this is interesting. :smile: It appears that I am looking for the generating function of a very particular sequence, although I hadn't realize that. So finding a closed form seems against the odds...

When 0 < x < 1, we can be sure that the following infinite product converges. \[ \prod_{n=1}^\infty (1 + x^n)\] But is there a closed form for it?

First, you can write the equation in this way \left[ \begin{array}{cc} x & y \end{array} \right] \cdot \left[ \begin{array}{cc} 1 & 2 \\ 2 & 1 \end{array} \right] \cdot \left[ \begin{array}{c} x \\ y \end{array} \right] = 12 Now, you have to diagonalize the symmetric matrix...

Thanks!

It's easy to see that \sum_{n=2}^{\infty}\frac{1}{lnn} does not converge. But what happens to \sum_{n=2}^{\infty}\frac{1}{(lnn)^k} with k > 1 and why? Can anybody help?

Thanks, your help was really valueable:!) . Following the links, I found this: http://www.acm.caltech.edu/~mlatini/research/qr_alg-feb04.pdf" As eigenvalues come in conjugate pairs, QR apparently fails (no dominant eigenvalue exists). However, instead of generating a single eigenvalue...

Let A be a matrix with real elements. The problem is to estimate eigenvalues of A, real and complex. QR algorithm is fine for real eigenvalues, but obviously fails to converge on complex eigenvalues... So, I'm looking for an alternative that could provide an estimate for complex eigenvalues of...