In mathematical analysis, the Dirichlet kernel, is the collection of periodic functions defined as D n ( x ) = ∑ k = − n n e i k x = ( 1 + 2 ∑ k = 1 n cos ( k x ) ) = sin ( ( n + 1 / 2 ) x ) sin ( x / 2 ) , {\displaystyle D_{n}(x)=\sum _{k=-n}^{n}e^{ikx}=\left(1+2\sum _{k=1}^{n}\cos(kx)\right)={\frac {\sin \left(\left(n+1/2\right)x\right)}{\sin(x/2)}},} where n is any nonnegative integer. The kernel functions are periodic with period 2 π {\displaystyle 2\pi } .
In mathematical analysis, the Dirichlet kernel, is the collection of periodic functions defined as D n ( x ) = ∑ k = − n n e i k x = ( 1 + 2 ∑ k = 1 n cos ( k x ) ) = sin ( ( n + 1 / 2 ) x ) sin ( x / 2 ) , {\displaystyle D_{n}(x)=\sum _{k=-n}^{n}e^{ikx}=\left(1+2\sum _{k=1}^{n}\cos(kx)\right)={\frac {\sin \left(\left(n+1/2\right)x\right)}{\sin(x/2)}},} where n is any nonnegative integer. The kernel functions are periodic with period 2 π {\displaystyle 2\pi } .
Source: Wikipedia "Dirichlet kernel" · CC BY-SA 4.0
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