DLMF:18.17.E19 (Q5760)

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DLMF:18.17.E19
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    Defining formula
    ∫ - 1 1 P n ⁡ ( x ) ⁢ e i ⁢ x ⁢ y ⁢ d x = i n ⁢ 2 ⁢ π y ⁢ J n + 1 2 ⁡ ( y ) , superscript subscript 1 1 Legendre-spherical-polynomial 𝑛 𝑥 superscript 𝑒 𝑖 𝑥 𝑦 𝑥 superscript 𝑖 𝑛 2 𝜋 𝑦 Bessel-J 𝑛 1 2 𝑦 {\displaystyle{\displaystyle\int_{-1}^{1}P_{n}\left(x\right)e^{ixy}\mathrm{d}x% =i^{n}\sqrt{\frac{2\pi}{y}}J_{n+\frac{1}{2}}\left(y\right),}}
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    DLMF id
    DLMF:18.17.E19
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