# Rush

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"The quieter you become, the more you are able to hear..."

# 50 Questions

 13 Does $\bigcap_{n=1}^{+\infty}(-\frac{1}{n},\frac{1}{n}) = \varnothing$? 9 Is $f(z)$ a constant in $\Bbb{C}$? 8 Funny integral inequality 8 Why is the determinant of a symplectic matrix 1? 6 Is the expression $\sum_{n=1}^{\infty}\prod_{k=1}^{n}\left(1-\frac{2}{3k}\right)$ bounded?

# 985 Reputation

 +15 number of zeros of function $\prod_{n=1}^{\infty}\left(1-\frac{z^2}{n^2}\right)-1$ +15 Do there exist some non-constant holomorphic functions such that the sum of the modulus of them is a constant +10 An integral$\frac{1}{2\pi}\int_0^{2\pi}\log|\exp(i\theta)-a|\text{d}\theta=0$ which I can calculate but can't understand it. +5 Is the remainder of the Taylor series of $\exp(x)$ negative when $x<0$ and $n$ is even?

 2 A matrix inequality 2 Whether Product of a Negative Definite Matrix and Positive Definite Matrix is Negative Definite? 2 Prove $\lim _{x \to 0} \sin(\frac{1}{x}) \ne 0$ 1 show particular solution satisfies the initial value problem 1 Eigen vector proof: $cI=A$ if $A$ has all non 0 eigenvetors

# 32 Tags

 5 linear-algebra × 11 1 homework × 2 5 matrices × 7 1 integration × 2 3 real-analysis × 5 1 differential-equations 2 limit 1 eigenvectors 2 proof-writing 1 eigenvalues

# 11 Accounts

 Mathematics 985 rep 9 English Language & Usage 114 rep 3 Stack Overflow 111 rep 3 Unix & Linux 101 rep 1 Theoretical Computer Science 101 rep 1