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Results tagged with riemann-zeta-function
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user 512896
The Riemann zeta function is the function of one complex variable $s$ defined by the series $\zeta(s) = \sum_{n \geq 1} \frac{1}{n^s}$ when $\operatorname{Re}(s)>1$. It admits a meromorphic continuation to $\mathbb{C}$ with only a simple pole at $1$. This function satisfies a functional equation relating the values at $s$ and $1-s$. This is the most simple example of an $L$-function and a central object of number theory.
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Are these continued fractions for the "tails" of $\zeta(3)$ and of the Catalan constant known?
I am very happy to find the "tails" formula of $\zeta(3)$ here. I have discovered the "tails" formula of $\eta(2)$ and $\beta(2)$ (Catalan's constant). You should be able to find these two similar for …
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