DLMF:18.37.E8 (Q6056)

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DLMF:18.37.E8
No description defined

    Statements

    Defining formula
    ∬ 0 < y < x < 1 P m , n α , β , γ ⁡ ( x , y ) ⁢ P j , ℓ α , β , γ ⁡ ( x , y ) ⁢ ( 1 - x ) α ⁢ ( x - y ) β ⁢ y γ ⁢ d x ⁢ d y = 0 , subscript double-integral 0 𝑦 𝑥 1 triangle-orthogonal-polynomial-P 𝛼 𝛽 𝛾 𝑚 𝑛 𝑥 𝑦 triangle-orthogonal-polynomial-P 𝛼 𝛽 𝛾 𝑗 ℓ 𝑥 𝑦 superscript 1 𝑥 𝛼 superscript 𝑥 𝑦 𝛽 superscript 𝑦 𝛾 𝑥 𝑦 0 {\displaystyle{\displaystyle\iint\limits_{0<y<x<1}P^{\alpha,\beta,\gamma}_{m,n% }\left(x,y\right)P^{\alpha,\beta,\gamma}_{j,\ell}\left(x,y\right)\*(1-x)^{% \alpha}(x-y)^{\beta}y^{\gamma}\mathrm{d}x\mathrm{d}y=0,}}
    0 references
    DLMF id
    DLMF:18.37.E8
    0 references
    constraint
    n ≠ ℓ 𝑛 ℓ {\displaystyle{\displaystyle n\neq\ell}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    triangle polynomial
    Defining formula
    P m , n α , β , γ ⁡ ( missing , missing ) triangle-orthogonal-polynomial-P 𝛼 𝛽 𝛾 𝑚 𝑛 missing missing {\displaystyle{\displaystyle P^{\NVar{\alpha},\NVar{\beta},\NVar{\gamma}}_{% \NVar{m},\NVar{n}}\left(missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C18.S37.E7.m2aadec
    0 references
    Q11743
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1cdec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1adec
    0 references
    Q11730
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1gdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1gdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1cdec
    0 references
     
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