/sci/ - Science & Math

Formula thread! Post sweet formulas.

Anyone know how I could find a reasonable formula for <span class="math"> \sum_{t=1}^{2^{n-2}}\frac{\sin(Xt)}{t}[/spoiler]? Here <span class="math">X=4\pi (3/2)^n[/spoiler]; basically, it's the partial sum of the Fourier series of <span class="math">\lfloor x \rfloor [/spoiler] for some <span class="math">x[/spoiler]. I haven't been able to find anything about partial sums of Fourier series that's been terribly helpful, and although I did read a paper on random harmonic series, it's not exactly applicable as even though the sines fluctuate, I need the magnitudes of the sine function to get a bound for my application.

Pic unrelated, although still pretty cool.

>>6219950
fuck me.