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statisticaloddsandends.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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| | | | | I recently came across this theorem on John Cook's blog that I wanted to keep for myself for future reference: Theorem. Let $latex f$ be a function so that $latex f^{(n+1)}$ is continuous on $latex [a,b]$ and satisfies $latex |f^{(n+1)}(x)| \leq M$. Let $latex p$ be a polynomial of degree $latex \leq n$ that interpolates... | |
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gwhphotos2.wordpress.com
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| | | | | Hockey stick chair Be sure to visit pull up a seat for more interesting photos, and/or to share yours. | |
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recordingnature.wordpress.com
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| | | I so wanted to have this blog on wordpress. But was not at all comfortable with it. Moved to blogger http://recordingnature.blogspot.in/ | ||
