DLMF:1.8.E4 (Q258)

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DLMF:1.8.E4
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    Statements

    Defining formula
    c n = 1 2 ⁢ π ⁢ ∫ - π π f ⁢ ( x ) ⁢ e - i ⁢ n ⁢ x ⁢ d x . subscript 𝑐 𝑛 1 2 𝜋 subscript superscript 𝜋 𝜋 𝑓 𝑥 superscript 𝑒 𝑖 𝑛 𝑥 𝑥 {\displaystyle{\displaystyle c_{n}=\frac{1}{2\pi}\int^{\pi}_{-\pi}f(x)e^{-inx}% \mathrm{d}x.}}
    0 references
    DLMF id
    DLMF:1.8.E4
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
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