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Results tagged with cv.complex-variables
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user 46140
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
15
votes
Accepted
Multiple roots of polynomials with coefficients $\pm 1$
Question P. Can a polynomial $P(x)=\sum_{n=0}^ma_nx^n$ with coefficients $a_n\in\{-1,1\}$ (and $P(1)=0$) have a multiple root in the interval $(\tfrac12,1)$?
Yes. The following four Littlewood polyn …
- 7,226
3
votes
Seeking an integral formulation for an algebraic function
$$\frac{1}{2\pi}\int_0^\infty \frac{\sqrt t}{(t + a^2) (t - x + \tfrac14)} \textrm{d}t = \frac{1}{2a + \sqrt{1 - 4x}}$$
So just take $a = \tfrac12 + x$.
- 7,226
4
votes
Accepted
Another combinatorial identity
Subst $k = p - 2n \ge 0$ and $s = r - i$ to get the symmetric
$$\sum_{s \ge 0,i \ge 0} [s + i \le 2n + k] \frac{(-1)^{s+i} (3n+k-s-i-1)! (2n^2 + nk - is)}{i!(n-i)!(2n + k-i)! s!(n-s)!(2n + k-s)!}$$
Bu …
- 7,226