DLMF:18.18.E39 (Q5829): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1aldec

Revision as of 01:28, 2 January 2020

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DLMF:18.18.E39
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    Statements

    Defining formula
    ∑ ℓ = 0 n ( n ℓ ) ⁢ H ℓ ⁡ ( 2 1 2 ⁢ x ) ⁢ H n - ℓ ⁡ ( 2 1 2 ⁢ y ) = 2 1 2 ⁢ n ⁢ H n ⁡ ( x + y ) , superscript subscript ℓ 0 𝑛 binomial 𝑛 ℓ Hermite-polynomial-H ℓ superscript 2 1 2 𝑥 Hermite-polynomial-H 𝑛 ℓ superscript 2 1 2 𝑦 superscript 2 1 2 𝑛 Hermite-polynomial-H 𝑛 𝑥 𝑦 {\displaystyle{\displaystyle\sum_{\ell=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{\ell}H% _{\ell}\left(2^{\frac{1}{2}}x\right)H_{n-\ell}\left(2^{\frac{1}{2}}y\right)=2^% {\frac{1}{2}n}H_{n}\left(x+y\right),}}
    0 references
    DLMF id
    DLMF:18.18.E39
    0 references
    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.m2agdec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1acdec
    0 references
    Q11743
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1ddec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1zdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1aldec
    0 references
     
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