We know if $x$ is not an integer we have
$$\left \lfloor x \right \rfloor=x-\frac{1}{2}+\frac{1}{\pi }\sum_{k=1}^{\infty}\frac{\sin(2\pi kx)}{k}$$
Is there an series expansion of floor function which contains the situation of $x$ being an integer?
2026-03-27 10:45:57.1774608357
Full series expansion of the floor function
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