DLMF:14.17.E14 (Q4895)

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DLMF:14.17.E14
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    - 1 1 𝖯 ν ( x ) 𝖰 λ ( x ) d x = 2 sin ( ν π ) cos ( λ π ) ( ψ ( ν + 1 ) - ψ ( λ + 1 ) ) + π cos ( ( λ - ν ) π ) - π π ( λ - ν ) ( λ + ν + 1 ) , superscript subscript 1 1 shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑥 shorthand-Ferrers-Legendre-Q-first-kind 𝜆 𝑥 𝑥 2 𝜈 𝜋 𝜆 𝜋 digamma 𝜈 1 digamma 𝜆 1 𝜋 𝜆 𝜈 𝜋 𝜋 𝜋 𝜆 𝜈 𝜆 𝜈 1 {\displaystyle{\displaystyle\int_{-1}^{1}\mathsf{P}_{\nu}\left(x\right)\mathsf% {Q}_{\lambda}\left(x\right)\mathrm{d}x=\frac{2\sin\left(\nu\pi\right)\cos\left% (\lambda\pi\right)\left(\psi\left(\nu+1\right)-\psi\left(\lambda+1\right)% \right)+\pi\cos\left((\lambda-\nu)\pi\right)-\pi}{\pi(\lambda-\nu)(\lambda+\nu% +1)},}}
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    DLMF:14.17.E14
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