DLMF:14.17.E12 (Q4893)

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DLMF:14.17.E12
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    - 1 1 𝖰 ν ( x ) 𝖰 λ ( x ) d x = ( ( ψ ( ν + 1 ) - ψ ( λ + 1 ) ) ( 1 + cos ( ν π ) cos ( λ π ) ) + 1 2 π sin ( ( λ - ν ) π ) ) ( λ - ν ) ( λ + ν + 1 ) , superscript subscript 1 1 shorthand-Ferrers-Legendre-Q-first-kind 𝜈 𝑥 shorthand-Ferrers-Legendre-Q-first-kind 𝜆 𝑥 𝑥 digamma 𝜈 1 digamma 𝜆 1 1 𝜈 𝜋 𝜆 𝜋 1 2 𝜋 𝜆 𝜈 𝜋 𝜆 𝜈 𝜆 𝜈 1 {\displaystyle{\displaystyle\int_{-1}^{1}\mathsf{Q}_{\nu}\left(x\right)\mathsf% {Q}_{\lambda}\left(x\right)\mathrm{d}x=\frac{\left((\psi\left(\nu+1\right)-% \psi\left(\lambda+1\right))(1+\cos\left(\nu\pi\right)\cos\left(\lambda\pi% \right))+\frac{1}{2}\pi\sin\left((\lambda-\nu)\pi\right)\right)}{(\lambda-\nu)% (\lambda+\nu+1)},}}
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