DLMF:18.15.E27 (Q5722): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: DLMF:18.15.E26 / rank
 
Normal rank
Property / Symbols used: DLMF:18.15.E26 / qualifier
 
Defining formula:

ω n , m ⁢ ( x ) subscript 𝜔 𝑛 𝑚 𝑥 {\displaystyle{\displaystyle\omega_{n,m}(x)}}

\omega_{n,m}(x)
Property / Symbols used: DLMF:18.15.E26 / qualifier
 
xml-id: C18.S15.XMD21.m1adec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1jdec

Latest revision as of 15:40, 2 January 2020

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DLMF:18.15.E27
No description defined

    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
    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
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2afdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    Q11730
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1qdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1qdec
    0 references
    DLMF:18.15.E26
    Defining formula
    ω n , m ⁢ ( x ) subscript 𝜔 𝑛 𝑚 𝑥 {\displaystyle{\displaystyle\omega_{n,m}(x)}}
    xml-id
    C18.S15.XMD21.m1adec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1jdec
    0 references
     
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