DLMF:18.35.E5 (Q6044)

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DLMF:18.35.E5
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    Statements

    Defining formula
    ∫ - 1 1 P n ( λ ) ⁡ ( x ; a , b ) ⁢ P m ( λ ) ⁡ ( x ; a , b ) ⁢ w ( λ ) ⁢ ( x ; a , b ) ⁢ d x = 0 , superscript subscript 1 1 Pollaczek-polynomial-P 𝜆 𝑛 𝑥 𝑎 𝑏 Pollaczek-polynomial-P 𝜆 𝑚 𝑥 𝑎 𝑏 superscript 𝑤 𝜆 𝑥 𝑎 𝑏 𝑥 0 {\displaystyle{\displaystyle{\int_{-1}^{1}P^{(\lambda)}_{n}\left(x;a,b\right)P% ^{(\lambda)}_{m}\left(x;a,b\right)w^{(\lambda)}(x;a,b)\mathrm{d}x=0},}}
    0 references
    DLMF id
    DLMF:18.35.E5
    0 references
    constraint
    n ≠ m 𝑛 𝑚 {\displaystyle{\displaystyle n\neq m}}
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    Symbols used
    Pollaczek polynomial
    Defining formula
    P n ( λ ) ⁡ ( x ; a , b ) Pollaczek-polynomial-P 𝜆 𝑛 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};% \NVar{a},\NVar{b}\right)}}
    xml-id
    C18.S35.E4.m2acdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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    Q11729
    Defining formula
    w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    xml-id
    C18.S1.XMD10.m1dec
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    Q11730
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1dec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1bdec
    0 references
     
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