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Results tagged with inequalities
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user 48831
for questions involving inequalities, upper and lower bounds.
5
votes
(Sharp) inequality for Beta function
One can also use Jensen's inequality. Let (for $\sigma>0$) $G_\sigma$ denote a random variable with $\Gamma(1,\sigma)$-distribution, i.e. having Lebesgue density
$$f_\sigma(t)=\frac{t^{\sigma-1}}{\G …
- 3,255
24
votes
Binomial again, and again
Here is a proof which doesn't use the identity $\int_{-\infty}^\infty {n \choose x}\,dx= 2^n$:
Using the representation ${ n \choose x}=\frac{1}{2\pi}\int_{-\pi}^\pi e^{-ixt}\left(1+e^{it}\right)^n\, …
- 3,255