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Results tagged with growth-rate
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user 36721
9
votes
Accepted
Oscillation of monotone real-analytic function
An elementary example is given by the formula
$$f(x)=\sum_{k=1}^\infty k!\,\Phi(x-k!)$$
for real $x>1$, where $\Phi$ is the standard normal cumulative distribution function. Then the function $f$ is r …
- 128k
1
vote
Accepted
Inferring polynomial rate of convergence from polynomial bound
The answer is no (assuming that $\|x\|:=x$ for real $x\ge0$). Indeed, as noted by mathworker21, your condition on the existence of $p$ is always satisfied, by choosing, e.g., $p(t)=c+t$ with $c:=\sup_ …
- 128k
2
votes
Proving a sum to be sublinear in growth
$\newcommand{\al}{\alpha}
\newcommand{\de}{\delta}
\newcommand{\De}{\Delta}
\newcommand{\ep}{\epsilon}
\newcommand{\ga}{\gamma}
\newcommand{\Ga}{\Gamma}
\newcommand{\la}{\lambda}
\newcommand{\Si}{\Sig …
- 128k