# Questions tagged [divergent-series]

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### Discrete entropy of the integer part of a random variable

Let $X$ be a real valued random variable. Of course, the integer part $\lfloor X \rfloor$ of $X$ is a discrete random variable taking values in $\mathbb{Z}$. We can therefore define its discrete ...
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### Numerical algorithm for extracting the coefficients of transseries

Assume a function $f(x)$ is given numerically for $x>0$, i.e. for any $x>0$ there is a numerical procedure to obtain $f(x)$ to any desired precision. Also assume that the function $f(x)$ has a ...
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### A family of divergent series

Is it reasonable to assert that $0^k - 1^k - 2^k + 3^k - 4^k + 5^k + 6^k - 7^k - ... = 0$ for all $k > 1$? Here the signs are given by the Thue-Morse sequence; that is, the sign of $m^k$ is $+$ or ...
Let $f : A \to A \subseteq \mathbb R$ be a real function with a fixed point $a_0 = f(a_0)$ which is not attractive. Let $f^k = f \circ f \circ ... \circ f$ be the $k^{th}$ iterate of $f$ (with the ...