DLMF:18.12.E16 (Q5658)

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DLMF:18.12.E16
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    Statements

    Defining formula
    e x ⁢ z - 1 2 ⁢ z 2 = ∑ n = 0 ∞ 𝐻𝑒 n ⁡ ( x ) n ! ⁢ z n . superscript 𝑒 𝑥 𝑧 1 2 superscript 𝑧 2 superscript subscript 𝑛 0 Hermite-polynomial-He 𝑛 𝑥 𝑛 superscript 𝑧 𝑛 {\displaystyle{\displaystyle e^{xz-\frac{1}{2}z^{2}}=\sum_{n=0}^{\infty}\frac{% \mathit{He}_{n}\left(x\right)}{n!}z^{n}.}}
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    DLMF id
    DLMF:18.12.E16
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    Symbols used
    Q11525
    Defining formula
    𝐻𝑒 n ⁡ ( x ) Hermite-polynomial-He 𝑛 𝑥 {\displaystyle{\displaystyle\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r14.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
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