DLMF:1.17.E20 (Q679)

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DLMF:1.17.E20
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    Statements

    Defining formula
    δ n ⁡ ( x - a ) = 1 2 ⁢ π ⁢ ∑ k = - n n e i ⁢ k ⁢ ( x - a ) ( = sin ⁡ ( ( n + 1 2 ) ⁢ ( x - a ) ) 2 ⁢ π ⁢ sin ⁡ ( 1 2 ⁢ ( x - a ) ) ) , Dirac-delta-sequence 𝑛 𝑥 𝑎 annotated 1 2 𝜋 superscript subscript 𝑘 𝑛 𝑛 superscript 𝑒 𝑖 𝑘 𝑥 𝑎 absent 𝑛 1 2 𝑥 𝑎 2 𝜋 1 2 𝑥 𝑎 {\displaystyle{\displaystyle\delta_{n}\left(x-a\right)=\frac{1}{2\pi}\sum_{k=-% n}^{n}e^{ik(x-a)}\left(=\frac{\sin\left((n+\frac{1}{2})(x-a)\right)}{2\pi\sin% \left(\frac{1}{2}(x-a)\right)}\right),}}
    0 references
    DLMF id
    DLMF:1.17.E20
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    Symbols used
    Q10917
    Defining formula
    δ n ⁡ ( x ) Dirac-delta-sequence 𝑛 𝑥 {\displaystyle{\displaystyle\delta_{n}\left(\NVar{x}\right)}}
    xml-id
    C1.S17.SS1.p1.m6aedec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aldec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2agdec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
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