Formula for the floor function – math.stackexchange.com

Formula for the floor function – math.stackexchange.com

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I found the following formula for the floor function: $$\lfloor x \rfloor = -\frac12+x+\frac{\arctan(\cot\pi x)}{\pi}$$ for all $x$ not an integer. My question is where I can find the proof of this ...

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