: Mathematics: Dirichlet kernel

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Dirichlet kernel

In mathematical analysis, the Dirichlet kernel, named after the German mathematician Peter Gustav Lejeune Dirichlet, is the collection of periodic functions defined as ${\\displaystyle D_{n}(x)=\\sum _{k=-n}^{n}e^{ikx}=\\left(1+2\\sum _{k=1}^{n}\\cos(kx)\ ight)={\ rac {\\sin \\left(\\left(n+1/2\ ight)x\ ight)}{\\sin(x/2)}},}$ where $n$ is any nonnegative integer. The kernel functions are periodic with period ${\\displaystyle 2\\pi }$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Dirichlet_kernel)

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