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mikespivey.wordpress.com | ||
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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... | |
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mathematicaloddsandends.wordpress.com
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| | | | | The function $latex f(x) = x \log x$ occurs in various places across math/statistics/machine learning (e.g. in the definition of entropy), and I thought I'd put a list of properties of the function here that I've found useful. Here is a plot of the function: $latex f$ is defined on $latex (0, \infty)$. The only... | |
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selondonzines.wordpress.com
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| | | | | Saturday 1st of November 2014! SOUTH EAST LONDON ZINE FEST! Apply now for a table. £5 a spot. Deadline for applications is 15th of October. To apply visit 'Apply for a table!' tab ^^^ selzf x | |
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runswiththedug.wordpress.com
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| | | Visit the post for more. | ||
