DLMF:18.18.E24 (Q5814)

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DLMF:18.18.E24
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    Statements

    Defining formula
    b n , ℓ = ( n ℓ ) ⁢ ( n + α + β + 1 ) ℓ ⁢ ( - β - n ) n - ℓ 2 ℓ ⁢ ( α + 1 ) n , subscript 𝑏 𝑛 ℓ binomial 𝑛 ℓ Pochhammer 𝑛 𝛼 𝛽 1 ℓ Pochhammer 𝛽 𝑛 𝑛 ℓ superscript 2 ℓ Pochhammer 𝛼 1 𝑛 {\displaystyle{\displaystyle b_{n,\ell}=\genfrac{(}{)}{0.0pt}{}{n}{\ell}\frac{% {\left(n+\alpha+\beta+1\right)_{\ell}}{\left(-\beta-n\right)_{n-\ell}}}{2^{% \ell}{\left(\alpha+1\right)_{n}}},}}
    0 references
    DLMF id
    DLMF:18.18.E24
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1ajdec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1abdec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1mdec
    0 references
     
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