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| | aperiodical.com
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| | This week, Katie and Paul are blogging from the Heidelberg Laureate Forum - a week-long maths conference where current young researchers in maths and computer science can meet and hear talks by top...
| | thatsmaths.com
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| | The Riemann Hypothesis Perhaps the greatest unsolved problem in mathematics is to explain the distribution of the prime numbers. The overall ``thinning out'' of the primes less than some number $latex {N}&fg=000000$, as $latex {N}&fg=000000$ increases, is well understood, and is demonstrated by the Prime Number Theorem (PNT). In its simplest form, PNT states that...
| | ianwrightsite.wordpress.com
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| | Riemann's Zeta function is an infinite sublation of Hegelian integers.
| | 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...