DLMF:1.17.E23 (Q682)

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DLMF:1.17.E23
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    Statements

    test
    δ ⁡ ( x - a ) = e - ( x + a ) / 2 ⁢ ∑ k = 0 ∞ L k ⁡ ( x ) ⁢ L k ⁡ ( a ) . Dirac-delta 𝑥 𝑎 superscript 𝑒 𝑥 𝑎 2 superscript subscript 𝑘 0 shorthand-Laguerre-polynomial-L 𝑘 𝑥 shorthand-Laguerre-polynomial-L 𝑘 𝑎 {\displaystyle{\displaystyle\delta\left(x-a\right)=e^{-(x+a)/2}\sum_{k=0}^{% \infty}L_{k}\left(x\right)L_{k}\left(a\right).}}
    0 references
    DLMF id
    DLMF:1.17.E23
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    Symbols used
    Q10915
    test
    δ ⁡ ( x - a ) Dirac-delta 𝑥 𝑎 {\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}
    xml-id
    C1.S17.SS1.p1.m2ajdec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aldec
    0 references
     
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