I would like to know a single (not piecewise) continuous approximation of $x \bmod 1$ which gets sharper the more you increase a constant $c$. I do not want a series like Fourier, but I do want something that uses continuous trigonometric functions (though $\arcsin$ is fine).
2026-03-25 12:26:04.1774441564
Continous, Non-Fourier, Trigonometric Approximation of the Fractional Part Function
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