DLMF:18.17.E44 (Q5785)

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DLMF:18.17.E44
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    test
    ∫ - 1 1 P n ⁡ ( x ) - P n ⁡ ( t ) | x - t | ⁢ d t = 2 ⁢ ( 1 + 1 2 + … + 1 n ) ⁢ P n ⁡ ( x ) , superscript subscript 1 1 Legendre-spherical-polynomial 𝑛 𝑥 Legendre-spherical-polynomial 𝑛 𝑡 𝑥 𝑡 𝑡 2 1 1 2 … 1 𝑛 Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle\int_{-1}^{1}\frac{P_{n}\left(x\right)-P_{n}\left(% t\right)}{|x-t|}\mathrm{d}t=2\left(1+\tfrac{1}{2}+\dots+\tfrac{1}{n}\right)P_{% n}\left(x\right),}}
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    DLMF id
    DLMF:18.17.E44
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    constraint
    - 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}}
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