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lucatrevisan.wordpress.com | ||
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stevensoojin.kim
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| | | | | A survey of Poincaré inequalities appearing outside of PDE. | |
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www.ethanepperly.com
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almostsuremath.com
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| | | | | The aim of this post is to motivate the idea of representing probability spaces as states on a commutative algebra. We will consider how this abstract construction relates directly to classical probabilities. In the standard axiomatization of probability theory, due to Kolmogorov, the central construct is a probability space $latex {(\Omega,\mathcal F,{\mathbb P})}&fg=000000$. This consists... | |
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ckrao.wordpress.com
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| | | In this post I would like to prove the following identity, motivated by this tweet. $latex \displaystyle n! \prod_{k=0}^n \frac{1}{x+k} = \frac{1}{x\binom{x+n}{n}} = \sum_{k=0}^n \frac{(-1)^k \binom{n}{k}}{x+k}$ The first of these equalities is straightforward by the definition of binomial coefficients. To prove the second, we make use of partial fractions. We write the expansion $latex \displaystyle... | ||
