query: How to show $ {\pi}^e 0$?
positive_passages.docid: 21003
positive_passages.text: Comparing $\pi^e$ and $e^\pi$ without calculating them
negative_passages.docid: 71054
negative_passages.text: How would you explain why $e^{i\pi}+1=0$ to a middle school student?
negative_passages.docid: 12433
negative_passages.text: How do $\pi^0$ particles exist?
negative_passages.docid: 105423
negative_passages.text: Why doesn't every integral from 0 to $2\pi$ equal zero?
negative_passages.docid: 156881
negative_passages.text: How prove this inequality $I=\int_{0}^{\sqrt{2\pi}}\sin{x^2}dx>0$
negative_passages.docid: 109295
negative_passages.text: Proving $1-\exp(-4x^2/ \pi) \ge \text{erf}(x)^2$
negative_passages.docid: 12402
negative_passages.text: Showing a function on $[0,1]$ is the zero function
negative_passages.docid: 43440
negative_passages.text: Complex Analysis: Showing analytic function is zero
negative_passages.docid: 106803
negative_passages.text: How to see $\cos x \leq \exp(-x^2/2)$ on $x \in [0,\pi/2]$?
negative_passages.docid: 34017
negative_passages.text: Show that $n^{\pi\left(2n\right)-\pi\left(n\right)}2$
negative_passages.docid: 3098
negative_passages.text: How are first digits of $\pi$ found?
negative_passages.docid: 109175
negative_passages.text: Why is it hard to prove whether $\pi+e$ is an irrational number?
negative_passages.docid: 115913
negative_passages.text: Zeros of exponential
negative_passages.docid: 139411
negative_passages.text: Finding $\pi$ factorial
negative_passages.docid: 40537
negative_passages.text: How to prove $\int_0^\infty e^{-x^2}cos(2bx) dx = \frac{\sqrt{\pi}}{2} e^{-b^2}$
negative_passages.docid: 12401
negative_passages.text: Is it standard to say $-i \log(-1)$ is $\pi$?
negative_passages.docid: 52943
negative_passages.text: How to show $\lim_{\epsilon \rightarrow 0} \frac{\epsilon}{x^2+\epsilon ^2} = \pi \delta (x)$?