query: Hint for proof of $\mathrm e^π>π^{\mathrm e}$
positive_passages.docid: 21003
positive_passages.text: Comparing $\pi^e$ and $e^\pi$ without calculating them
negative_passages.docid: 125209
negative_passages.text: Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
negative_passages.docid: 102738
negative_passages.text: Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction.
negative_passages.docid: 27086
negative_passages.text: proof for $\langle q| p \rangle = e^{ipq}$
negative_passages.docid: 101792
negative_passages.text: By expanding $e^x$ into a series prove the following inequality
negative_passages.docid: 2593
negative_passages.text: Proof for Mersenne primes?
negative_passages.docid: 63124
negative_passages.text: Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
negative_passages.docid: 129584
negative_passages.text: How prove $E|X|^p<\infty$ and $E|Y|^p<\infty$, if $E|X+Y|^p<\infty$
negative_passages.docid: 106609
negative_passages.text: Show that $e^{iy} = 1 + iy + \frac{\mu_1 y^2}{2}$ for all $y \in \mathbb{R}$ with $|\mu_1| \leq 1$
negative_passages.docid: 120906
negative_passages.text: Is there a proof that $\pi \times e$ is irrational?
negative_passages.docid: 8311
negative_passages.text: Is there another proof for Euler–Mascheroni Constant?
negative_passages.docid: 38785
negative_passages.text: Prove previsibility and $E[X_{T \wedge n}] \le E[X_{S \wedge n}]$
negative_passages.docid: 2251
negative_passages.text: Can someone give me a hint on how to prove this?
negative_passages.docid: 120985
negative_passages.text: Prove that $\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$
negative_passages.docid: 94077
negative_passages.text: Proof of linear independence of $e^{at}$
negative_passages.docid: 90896
negative_passages.text: proof of inequality $e^x\le x+e^{x^2}$
negative_passages.docid: 34491
negative_passages.text: Is there a way to show that $\sqrt{p_{n}} < n$?