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Tagged with irrational-numbers reference-request
9 questions
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Ergodic Theory and Euler-Mascheroni Constant
I am highly interested in doing research on proving irrationality of some specific numbers like Euler-Mascheroni Constant or $\zeta(5)$. A professor guided me that arithmetic nature of constants are a ...
user288447
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Is $\sum_{n=1}^\infty\frac{S(n)}{n!}$ an irrational, where $S(n)$ denotes the sum of remainders function?
For each integer $n\geq 1$ we consider the arithmetic function $$S(n)=\sum_{k=1}^n n\text{ mod }k,\tag{1}$$
the sum of remainders function, the arithmetic function A004125 from the OEIS.
Example. We'...
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Chudnovsky algorithm and Pi precision
What are the precision/ number of correct Pi digits after N iterations of Chudnovsky algorithm. Looking for a formula (rather than a table) and reference.
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Fractional parts of two multiples [duplicate]
There is a theorem (I can't remember its name) saying that for any irrational number $x$ and any $0<a<b<1$, there exists a positive integer $n$ such that $\{nx\}\in (a,b)$, where $\{\cdot\}$ ...
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On Bailey–Borwein–Plouffe formula for irrational numbers
A BBP-type formula for an irrational number $\alpha$ in the integer base $b\geq 2$ is a formula in the form $\alpha=\Sigma_{k=0}^{\infty}\frac{1}{b^k}\frac{p(k)}{q(k)}$ ($p, q$ are polynomials in ...
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Transcendence of $\Gamma(1/3), \Gamma(1/4)$
This is a re-post from MSE as I did not get even a single comment there.
Wikipedia mentions that the transcendence of $\Gamma(1/3), \Gamma(1/4)$ was proved by G. V. Chudnovsky. Does anyone have a ...
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Computing all "suboptimal" rational approximations to $\pi/2$
I have an irrational number $\alpha$ ($\alpha=\frac\pi2$), and I would like to determine all integers $n\in[1,N]$ ($N=10^{16}$) that satisfy
$$ n \epsilon(n)^2 \leq \tau $$
where $\tau$ is a known ...
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Multiplying by irrational numbers in combinatorial problems
This is getting no attention on stackexchange.
Everybody knows that the number of derangements of a set of size $n$ is the nearest integer to $n!/e$.
It had escaped my attention until last week, ...
3
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$\mathbb{S}^2$ equivalent to frac$(n \alpha)$ equidistribution on $\mathbb{S}^1$
Let $\operatorname{frac}(x) = x - \lfloor x \rfloor$ be the fractional part of $x$.
Then, for $\alpha$ irrational, $\operatorname{frac}(n \alpha)$, $n=1,2,\ldots$, distributes
randomly in $[0,1)$, ...
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