DLMF:18.17.E7 (Q5748)

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DLMF:18.17.E7
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    test
    ( P n ⁡ ( x ) ) 2 + 4 ⁢ π - 2 ⁢ ( 𝖰 n ⁡ ( x ) ) 2 = 4 ⁢ π - 2 ⁢ ∫ 1 ∞ Q n ⁡ ( x 2 + ( 1 - x 2 ) ⁢ t ) ⁢ ( t 2 - 1 ) - 1 2 ⁢ d t , superscript Legendre-spherical-polynomial 𝑛 𝑥 2 4 superscript 𝜋 2 superscript shorthand-Ferrers-Legendre-Q-first-kind 𝑛 𝑥 2 4 superscript 𝜋 2 superscript subscript 1 shorthand-Legendre-Q-second-kind 𝑛 superscript 𝑥 2 1 superscript 𝑥 2 𝑡 superscript superscript 𝑡 2 1 1 2 𝑡 {\displaystyle{\displaystyle\left(P_{n}\left(x\right)\right)^{2}+4\pi^{-2}% \left(\mathsf{Q}_{n}\left(x\right)\right)^{2}=4\pi^{-2}\*\int_{1}^{\infty}Q_{n% }\left(x^{2}+(1-x^{2})t\right)(t^{2}-1)^{-\frac{1}{2}}\mathrm{d}t,}}
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    DLMF id
    DLMF:18.17.E7
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