DLMF:1.17.E18 (Q677)

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DLMF:1.17.E18
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    Statements

    Defining formula
    ∫ - π π ϕ ⁢ ( x ) ⁢ ( 1 2 ⁢ π ⁢ ∑ k = - ∞ ∞ e i ⁢ k ⁢ ( x - a ) ) ⁢ d x = ϕ ⁢ ( a ) . superscript subscript 𝜋 𝜋 italic-ϕ 𝑥 1 2 𝜋 superscript subscript 𝑘 superscript 𝑒 𝑖 𝑘 𝑥 𝑎 𝑥 italic-ϕ 𝑎 {\displaystyle{\displaystyle\int_{-\pi}^{\pi}\phi(x)\left(\frac{1}{2\pi}\sum_{% k=-\infty}^{\infty}e^{ik(x-a)}\right)\mathrm{d}x=\phi(a).}}
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    DLMF id
    DLMF:1.17.E18
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