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→Non-smooth functions: The Square Wave was missing its Fourier Series, The Sawtooth Wave had the wrong Fourier Series, and the Triangle Wave's Fourier Series confused two variables i and n, and had incorrect bounds for its summation. I also forgot to mention in the section on Cycloids that r was the radius of the circle. |
→Non-smooth functions: Added a formula and Fourier series for the Pulse Wave, as well as made the formula for the cycloid more consistent with the standards set above. |
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|| [[Square wave]] || <math> \sgn\left(\sin \frac{2\pi x}{p} \right) </math> ||<math> \frac4\pi\sum_{n\,\mathrm{odd}}^\infty\frac1n\sin\left(\frac{2n\pi x}{p}\right) </math>|| non-continuous
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|| [[Cycloid]] ||<math>
<small>
<small>its real valued inverse
<small>circle.</small>▼
| - || non-continuous first derivative
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|| [[Pulse wave ]] ||<math>H(\cos\Bigl(\frac{2\pi x}{p}\Bigr)-\cos\Bigl(\frac{\pi
<small>where ''H'' is the Heaviside Step Function and t is</small>
|<math>\frac{t}{p} + \sum_{n=1}^{\infty} \frac{2}{n\pi} \sin\left(\frac{\pi nt}{p}\right) \cos\left(\frac{2\pi n x}{p}\right)</math>|| non-continuous
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