DLMF:1.17.E20 (Q679)

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DLMF:1.17.E20
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    Statements

    Defining formula
    δ n ⁡ ( x - a ) = 1 2 ⁢ π ⁢ ∑ k = - n n e i ⁢ k ⁢ ( x - a ) ( = sin ⁡ ( ( n + 1 2 ) ⁢ ( x - a ) ) 2 ⁢ π ⁢ sin ⁡ ( 1 2 ⁢ ( x - a ) ) ) , Dirac-delta-sequence 𝑛 𝑥 𝑎 annotated 1 2 𝜋 superscript subscript 𝑘 𝑛 𝑛 superscript 𝑒 𝑖 𝑘 𝑥 𝑎 absent 𝑛 1 2 𝑥 𝑎 2 𝜋 1 2 𝑥 𝑎 {\displaystyle{\displaystyle\delta_{n}\left(x-a\right)=\frac{1}{2\pi}\sum_{k=-% n}^{n}e^{ik(x-a)}\left(=\frac{\sin\left((n+\frac{1}{2})(x-a)\right)}{2\pi\sin% \left(\frac{1}{2}(x-a)\right)}\right),}}
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    DLMF id
    DLMF:1.17.E20
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