DLMF:14.17.E18 (Q4899)

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DLMF:14.17.E18
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    Statements

    Defining formula
    ∫ 1 ∞ P ν ⁡ ( x ) ⁢ Q λ ⁡ ( x ) ⁢ d x = 1 ( λ - ν ) ⁢ ( ν + λ + 1 ) , superscript subscript 1 shorthand-Legendre-P-first-kind 𝜈 𝑥 shorthand-Legendre-Q-second-kind 𝜆 𝑥 𝑥 1 𝜆 𝜈 𝜈 𝜆 1 {\displaystyle{\displaystyle\int_{1}^{\infty}P_{\nu}\left(x\right)Q_{\lambda}% \left(x\right)\mathrm{d}x=\frac{1}{(\lambda-\nu)(\nu+\lambda+1)},}}
    0 references
    DLMF id
    DLMF:14.17.E18
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    constraint
    ℜ ⁡ λ > ℜ ⁡ ν > 0 𝜆 𝜈 0 {\displaystyle{\displaystyle\Re\lambda>\Re\nu>0}}
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aqdec
    0 references
     
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