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

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50 Questions

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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?

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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?

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9 Answers

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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

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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

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