DLMF:18.15.E28 (Q5723)

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DLMF:18.15.E28
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    Statements

    Defining formula
    H n ⁡ ( x ) = 2 1 4 ⁢ ( μ 2 - 1 ) ⁢ e 1 2 ⁢ μ 2 ⁢ t 2 ⁢ U ⁡ ( - 1 2 ⁢ μ 2 , μ ⁢ t ⁢ 2 ) ; Hermite-polynomial-H 𝑛 𝑥 superscript 2 1 4 superscript 𝜇 2 1 superscript 𝑒 1 2 superscript 𝜇 2 superscript 𝑡 2 parabolic-U 1 2 superscript 𝜇 2 𝜇 𝑡 2 {\displaystyle{\displaystyle H_{n}\left(x\right)=2^{\frac{1}{4}(\mu^{2}-1)}e^{% \frac{1}{2}\mu^{2}t^{2}}U\left(-\tfrac{1}{2}\mu^{2},\mu t\sqrt{2}\right);}}
    0 references
    DLMF id
    DLMF:18.15.E28
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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.m2aadec
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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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    Q11320
    Defining formula
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1adec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1rdec
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    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1kdec
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