DLMF:1.17.E18 (Q677)

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DLMF:1.17.E18
No description defined

    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).}}
    0 references
    DLMF id
    DLMF:1.17.E18
    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.m2ajdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1andec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3andec
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    Q10756
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1adec
    0 references
    Q10916
    Defining formula
    ϕ ⁢ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}
    xml-id
    C1.S17.XMD1.m1gdec
    0 references
     
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