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DLMF:18.18.E6 - MaRDI portal

DLMF:18.18.E6 (Q6493)

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DLMF:18.18.E6
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    Statements

    DLMF defining formula
    f ⁢ ( x ) = ∑ n = 0 ∞ d n ⁢ H n ⁡ ( x ) , 𝑓 𝑥 superscript subscript 𝑛 0 subscript 𝑑 𝑛 Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle f(x)=\sum_{n=0}^{\infty}d_{n}H_{n}\left(x\right),}}
    0 references
    constraint
    - ∞ < x < ∞ 𝑥 {\displaystyle{\displaystyle-\infty<x<\infty}}
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    Symbols used
    Hermite polynomial
    DLMF 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
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1edec
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    analytic function
    DLMF defining formula
    f ⁢ ( z ) 𝑓 𝑧 {\displaystyle{\displaystyle f(z)}}
    xml-id
    C18.S18.XMD1.m1edec
    0 references
    18.18.E7
    DLMF defining formula
    d n subscript 𝑑 𝑛 {\displaystyle{\displaystyle d_{n}}}
    xml-id
    C18.S18.XMD4.m1dec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1ddec
    0 references

    Identifiers

     
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