DLMF:18.14.E9 (Q5672)

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DLMF:18.14.E9
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    Statements

    Defining formula
    1 ( 2 n ⁢ n ! ) 1 2 ⁢ e - 1 2 ⁢ x 2 ⁢ | H n ⁡ ( x ) | ≤ 1 , 1 superscript superscript 2 𝑛 𝑛 1 2 superscript 𝑒 1 2 superscript 𝑥 2 Hermite-polynomial-H 𝑛 𝑥 1 {\displaystyle{\displaystyle\frac{1}{(2^{n}n!)^{\frac{1}{2}}}e^{-\frac{1}{2}x^% {2}}|H_{n}\left(x\right)|\leq 1,}}
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    DLMF id
    DLMF:18.14.E9
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    constraint
    - ∞ < x < ∞ 𝑥 {\displaystyle{\displaystyle-\infty<x<\infty}}
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    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.m2aadec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5agdec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1fdec
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