DLMF:1.8.E14 (Q268)

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DLMF:1.8.E14
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    Statements

    Defining formula
    ∑ n = - ∞ ∞ f ⁢ ( x + n ) = ∑ n = - ∞ ∞ e 2 ⁢ π ⁢ i ⁢ n ⁢ x ⁢ ∫ - ∞ ∞ f ⁢ ( t ) ⁢ e - 2 ⁢ π ⁢ i ⁢ n ⁢ t ⁢ d t . subscript superscript 𝑛 𝑓 𝑥 𝑛 subscript superscript 𝑛 superscript 𝑒 2 𝜋 𝑖 𝑛 𝑥 subscript superscript 𝑓 𝑡 superscript 𝑒 2 𝜋 𝑖 𝑛 𝑡 𝑡 {\displaystyle{\displaystyle\sum^{\infty}_{n=-\infty}f(x+n)=\sum^{\infty}_{n=-% \infty}e^{2\pi inx}\int^{\infty}_{-\infty}f(t)e^{-2\pi int}\mathrm{d}t.}}
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    DLMF id
    DLMF:1.8.E14
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
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