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4.2: Комплексна серія Фур'є
https://ukrayinska.libretexts.org/%D0%86%D0%BD%D0%B6%D0%B5%D0%BD%D0%B5%D1%80%D0%BD%D0%B0/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D1%82%D0%B5%D1%85%D0%BD%D1%96%D0%BA%D0%B0/%D0%92%D1%81%D1%82%D1%83%D0%BF%D0%BD%D0%B0_%D0%B5%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D1%82%D0%B5%D1%85%D0%BD%D1%96%D0%BA%D0%B0/%D0%95%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D1%82%D0%B5%D1%85%D0%BD%D1%96%D0%BA%D0%B0_(Johnson)/04%3A_%D0%A7%D0%B0%D1%81%D1%82%D0%BE%D1%82%D0%BD%D0%B8%D0%B9_%D0%B4%D0%BE%D0%BC%D0%B5%D0%BD/4.02%3A_%D0%9A%D0%BE%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D0%B0_%D1%81%D0%B5%D1%80%D1%96%D1%8F_%D0%A4%D1%83%D1%80'%D1%94
$c_{k}=\frac{1}{T}\int_{0}^{\frac{T}{2}}e^{-\left ( i\frac{2\pi kt}{T}\right )} dt-\frac{1}{T}\int_{\frac{T}{2}}^{T}e^{-\left ( i\frac{2\pi kt}{T}\right )} dt \nonumber$ \[\therefore \; \; \; \; \;... $c_{k}=\frac{1}{T}\int_{0}^{\frac{T}{2}}e^{-\left ( i\frac{2\pi kt}{T}\right )} dt-\frac{1}{T}\int_{\frac{T}{2}}^{T}e^{-\left ( i\frac{2\pi kt}{T}\right )} dt \nonumber$ $\therefore \; \; \; \; \; \frac{1}{T}\int_{0}^{T}s(t-\tau )e^{(-i)\frac{2\pi kt}{T}} dt=\frac{1}{T}e^{(-i)\frac{2\pi kt}{T}} \int_{-\tau }^{T-\tau }s(t)e^{(-i)\frac{2\pi kt}{T}} dt \nonumber$