DLMF:18.10.E7 (Q5631)

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DLMF:18.10.E7
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    Statements

    Defining formula
    H n ⁡ ( x ) = 2 n π 1 2 ⁢ ∫ - ∞ ∞ ( x + i ⁢ t ) n ⁢ e - t 2 ⁢ d t . Hermite-polynomial-H 𝑛 𝑥 superscript 2 𝑛 superscript 𝜋 1 2 superscript subscript superscript 𝑥 𝑖 𝑡 𝑛 superscript 𝑒 superscript 𝑡 2 𝑡 {\displaystyle{\displaystyle H_{n}\left(x\right)=\frac{2^{n}}{\pi^{\frac{1}{2}% }}\int_{-\infty}^{\infty}(x+it)^{n}e^{-t^{2}}\mathrm{d}t.}}
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    DLMF id
    DLMF:18.10.E7
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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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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
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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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