DLMF:1.17.E24 (Q683)

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DLMF:1.17.E24
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    Statements

    test
    δ ⁡ ( x - a ) = e - ( x 2 + a 2 ) / 2 π ⁢ ∑ k = 0 ∞ H k ⁡ ( x ) ⁢ H k ⁡ ( a ) 2 k ⁢ k ! . Dirac-delta 𝑥 𝑎 superscript 𝑒 superscript 𝑥 2 superscript 𝑎 2 2 𝜋 superscript subscript 𝑘 0 Hermite-polynomial-H 𝑘 𝑥 Hermite-polynomial-H 𝑘 𝑎 superscript 2 𝑘 𝑘 {\displaystyle{\displaystyle\delta\left(x-a\right)=\frac{e^{-(x^{2}+a^{2})/2}}% {\sqrt{\pi}}\sum_{k=0}^{\infty}\frac{H_{k}\left(x\right)H_{k}\left(a\right)}{2% ^{k}k!}.}}
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    DLMF id
    DLMF:1.17.E24
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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.m2akdec
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    Q10922
    test
    H n ⁡ ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r13.m2adec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2andec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2amdec
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    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q10756
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1fdec
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