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Dirichlet kernel

In mathematical analysis, the Dirichlet kernel, is the collection of periodic functions defined as Dn(x)=∑k=−nneikx=1+2∑k=1ncos⁡(kx)=sin⁡((n+1/2)x)sin⁡(x/2),{\displaystyle D_{n}(x)=\sum _{k=-n}^{n}e^{ikx}=1+2\sum _{k=1}^{n}\cos(kx)={\frac {\sin \left(\left(n+1/2 ight)x ight)}{\sin(x/2)}},}where n is any nonnegative integer.

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