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

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Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5amdec
Property / Symbols used
 
Property / Symbols used: Q11744 / rank
 
Normal rank
Property / Symbols used: Q11744 / qualifier
 
Defining formula:

ℓ ℓ {\displaystyle{\displaystyle\ell}}

\ell
Property / Symbols used: Q11744 / qualifier
 
xml-id: C18.S1.XMD4.m1ldec
Property / Symbols used
 
Property / Symbols used: Q11730 / rank
 
Normal rank
Property / Symbols used: Q11730 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11730 / qualifier
 
xml-id: C18.S1.XMD5.m1ddec
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.m1vdec
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.m1sdec

Latest revision as of 01:26, 2 January 2020

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DLMF:18.18.E23
No description defined

    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
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5amdec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1ldec
    0 references
    Q11730
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1ddec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1vdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1sdec
    0 references
     
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