DLMF:18.11.E7 (Q5641)

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DLMF:18.11.E7
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    Statements

    Defining formula
    lim n → ∞ ⁡ ( - 1 ) n ⁢ n 1 2 2 2 ⁢ n ⁢ n ! ⁢ H 2 ⁢ n ⁡ ( z 2 ⁢ n 1 2 ) = 1 π 1 2 ⁢ cos ⁡ z , subscript → 𝑛 superscript 1 𝑛 superscript 𝑛 1 2 superscript 2 2 𝑛 𝑛 Hermite-polynomial-H 2 𝑛 𝑧 2 superscript 𝑛 1 2 1 superscript 𝜋 1 2 𝑧 {\displaystyle{\displaystyle\lim_{n\to\infty}\frac{(-1)^{n}n^{\frac{1}{2}}}{2^% {2n}n!}H_{2n}\left(\frac{z}{2n^{\frac{1}{2}}}\right)=\frac{1}{\pi^{\frac{1}{2}% }}\cos z,}}
    0 references
    DLMF id
    DLMF:18.11.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.m2aadec
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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.m2adec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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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.m1bdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1fdec
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