# Questions tagged [chebyshev-function]

For questions about Chebyshev functions $\vartheta(x)$ and $\psi(x)$, which are often used in number theory. For questions about Chebyshev polynomials, use the (chebyshev-polynomials) tag.

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Question: If $p$ and $q$ are prime numbers how do I write $\sum\limits_{p \leq q \text{ prime}}\log (p-1)$ using Chebyshev's function(s) ? I would like to think $\sum\limits_{p \leq q \text{ prime}}... • 3,758 2 votes 0 answers 152 views ### Is the sequence:$S_n=\Im(n\cdot\exp(\frac{2\pi\cdot i}{\log_{n}(p_n\#)})):n\in\Bbb N$monotonic for$P_n>41893$? How many times does the sequence:$S_n=\Im\left(n\cdot\exp\left(\frac{2\pi\cdot i}{\log_{n}(p_n\#)}\right)\right):n\in\Bbb N$oscillate? I.e. is it monotonic increasing after$S_{4379}$which ... • 9,295 0 votes 1 answer 336 views ### Linear vs Orthogonal polynomial for fitting I am neither a mathematician nor do I possess a large knowledge in maths so this could also be completely false. But I read that if you use an orthogonal function like the Chebychev-polynomial to ... 0 votes 0 answers 41 views ### Finding new expectation using Chebyshev. I've tried to use similar questions for this, but I ended up with just a horrible answer. I have a question about a woman serving soup, she originally had 30 litres for 80 pupils, with expectation 0.... 0 votes 1 answer 75 views ### Question about the hint and answer.(inequality,and the relation between hint and question itself) Question: Given two sequences of random variables {$X;n=1,2,...$} and {$Y;n=1,2,...$} and a random variable$X$,suppose that with probability one$|X_n-X| \le Y_n$all$n$and that$E[Y_n] \to 0$as$...
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What's the sum of the inverses of the primorial numbers? Let the $n^{th}$ primorial number be the product of the first $n$ primes $\displaystyle n\#= \prod_{p\leq p_n}p$ So \$N\#=2,2\cdot3,2\cdot3\...