DLMF:18.12.E15 (Q5657)

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DLMF:18.12.E15
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    Statements

    Defining formula
    e 2 ⁢ x ⁢ z - z 2 = ∑ n = 0 ∞ H n ⁡ ( x ) n ! ⁢ z n , superscript 𝑒 2 𝑥 𝑧 superscript 𝑧 2 superscript subscript 𝑛 0 Hermite-polynomial-H 𝑛 𝑥 𝑛 superscript 𝑧 𝑛 {\displaystyle{\displaystyle e^{2xz-z^{2}}=\sum_{n=0}^{\infty}\frac{H_{n}\left% (x\right)}{n!}z^{n},}}
    0 references
    DLMF id
    DLMF:18.12.E15
    0 references
    Symbols used
    Q10922
    Defining formula
    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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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1ndec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ndec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1mdec
    0 references
     
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