DLMF:14.17.E2 (Q4883)

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DLMF:14.17.E2
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    ∫ ( 1 - x 2 ) μ / 2 ⁢ 𝖯 ν μ ⁡ ( x ) ⁢ d x = ( 1 - x 2 ) ( μ + 1 ) / 2 ( ν - μ ) ⁢ ( ν + μ + 1 ) ⁢ 𝖯 ν μ + 1 ⁡ ( x ) , superscript 1 superscript 𝑥 2 𝜇 2 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝑥 superscript 1 superscript 𝑥 2 𝜇 1 2 𝜈 𝜇 𝜈 𝜇 1 Ferrers-Legendre-P-first-kind 𝜇 1 𝜈 𝑥 {\displaystyle{\displaystyle\int\left(1-x^{2}\right)^{\mu/2}\mathsf{P}^{\mu}_{% \nu}\left(x\right)\mathrm{d}x=\frac{\left(1-x^{2}\right)^{(\mu+1)/2}}{(\nu-\mu% )(\nu+\mu+1)}\mathsf{P}^{\mu+1}_{\nu}\left(x\right),}}
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    DLMF:14.17.E2
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