DLMF:18.15.E27 (Q5722)

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DLMF:18.15.E27
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    Statements

    Defining formula
    H n ⁡ ( x ) = λ n ⁢ e 1 2 ⁢ x 2 ⁢ ( ∑ m = 0 M - 1 u m ⁢ ( x ) ⁢ cos ⁡ ω n , m ⁢ ( x ) μ 1 2 ⁢ m + O ⁡ ( 1 μ 1 2 ⁢ M ) ) , Hermite-polynomial-H 𝑛 𝑥 subscript 𝜆 𝑛 superscript 𝑒 1 2 superscript 𝑥 2 superscript subscript 𝑚 0 𝑀 1 subscript 𝑢 𝑚 𝑥 subscript 𝜔 𝑛 𝑚 𝑥 superscript 𝜇 1 2 𝑚 Big-O 1 superscript 𝜇 1 2 𝑀 {\displaystyle{\displaystyle H_{n}\left(x\right)=\lambda_{n}e^{\frac{1}{2}x^{2% }}\left(\sum_{m=0}^{M-1}\frac{u_{m}(x)\cos\omega_{n,m}(x)}{\mu^{\frac{1}{2}m}}% +O\left(\frac{1}{\mu^{\frac{1}{2}M}}\right)\right),}}
    0 references
    DLMF id
    DLMF:18.15.E27
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2agdec
    0 references
     
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