DLMF:18.18.E23 (Q5813): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
Defining formula:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10754 / qualifier
 
xml-id: C1.S2.SS1.m1aadec

Revision as of 01:25, 2 January 2020

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DLMF:18.18.E23
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    Statements

    Defining formula
    H m ⁡ ( x ) ⁢ H n ⁡ ( x ) = ∑ ℓ = 0 min ⁡ ( m , n ) ( m ℓ ) ⁢ ( n ℓ ) ⁢ 2 ℓ ⁢ ℓ ! ⁢ H m + n - 2 ⁢ ℓ ⁡ ( x ) . Hermite-polynomial-H 𝑚 𝑥 Hermite-polynomial-H 𝑛 𝑥 superscript subscript ℓ 0 𝑚 𝑛 binomial 𝑚 ℓ binomial 𝑛 ℓ superscript 2 ℓ ℓ Hermite-polynomial-H 𝑚 𝑛 2 ℓ 𝑥 {\displaystyle{\displaystyle H_{m}\left(x\right)H_{n}\left(x\right)=\sum_{\ell% =0}^{\min(m,n)}\genfrac{(}{)}{0.0pt}{}{m}{\ell}\genfrac{(}{)}{0.0pt}{}{n}{\ell% }2^{\ell}\ell!H_{m+n-2\ell}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.18.E23
    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.m2aedec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aadec
    0 references
     
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