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statisticaloddsandends.wordpress.com | ||
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hbfs.wordpress.com
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| | | | | $latex n!$ (and its logarithm) keep showing up in the analysis of algorithm. Unfortunately, it's very often unwieldy, and we use approximations of $latex n!$ (or $latex \log n!$) to simplify things. Let's examine a few! First, we have the most known of these approximations, the famous "Stirling formula": $latex \displaystyle n!=\sqrt{2\pi{}n}\left(\frac{n}{e}\right)^n\left(1+\frac{1}{12n}+\frac{1}{288n^2}-\frac{139}{51840n^3}-\cdots\right)$, Where the terms... | |
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juliawolffenotes.home.blog
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| | | | | Recently Terry Tao posted to the arXiv his paper Almost all Collatz orbits attain almost bounded values, which caused quite the stir on social media. For instance, this Reddit post about it is only a day old and already has nearly a thousand upvotes; Twitter is abuzz with tweets like Tim Gowers': (this sentiment seems... | |
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mathematicaloddsandends.wordpress.com
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| | | | | I recently learned of Craig's formula for the Gaussian Q-function from this blog post from John Cook. Here is the formula: Proposition (Craig's formula). Let $latex Z$ be a standard normal random variable. Then for any $latex z \geq 0$, defining $latex \begin{aligned} \mathbb{P}\{ Z \geq z\} = Q(z) = \dfrac{1}{\sqrt{2\pi}} \int_z^\infty \exp \left( -... | |
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educationechochamber.wordpress.com
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| | | Reblogged on WordPress.com | ||
