It looks elementary. But how can I evaluate in general integrals of the form $ \int_0^T \sum_{n\leq t^2} a_n dt $. Is there some general transformation law? To be concrete, take $a_n=1/n$. But I need a general rule.
Evaluate the integral with sum depending on variable of integration
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integration
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0you can compute that integral explicitly; note that $f(t)=\sum_{n\leq t^{2}} a_{n}$ is constant in every interval of the form $[\sqrt{k},\sqrt{k+1}[$ – 2017-02-20