1.15.E19 (Q530)

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1.15.E19
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    Statements

    DLMF defining formula
    F ⁢ ( n ) = 1 2 ⁢ π ⁢ ∫ 0 2 ⁢ π f ⁢ ( t ) ⁢ e - i ⁢ n ⁢ t ⁢ d t . 𝐹 𝑛 1 2 𝜋 subscript superscript 2 𝜋 0 𝑓 𝑡 superscript 𝑒 𝑖 𝑛 𝑡 𝑡 {\displaystyle{\displaystyle F(n)=\frac{1}{2\pi}\int^{2\pi}_{0}f(t)e^{-int}% \mathrm{d}t.}}
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    Symbols defined
    1.15.E19
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
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    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1pdec
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    Identifiers

     
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