DLMF:14.17.E4 (Q4885)

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Language	Label	Description	Also known as
English	DLMF:14.17.E4	No description defined

Statements

{\displaystyle{\displaystyle\int\frac{x}{\left(1-x^{2}\right)^{3/2}}\mathsf{P}% ^{\mu}_{\nu}\left(x\right)\mathsf{Q}^{\mu}_{\nu}\left(x\right)\mathrm{d}x=% \frac{1}{\left(1-4\mu^{2}\right)\left(1-x^{2}\right)^{1/2}}\left((1-2\mu^{2}+2% \nu(\nu+1))\mathsf{P}^{\mu}_{\nu}\left(x\right)\mathsf{Q}^{\mu}_{\nu}\left(x% \right)+(2\nu+1)(\mu-\nu-1)x(\mathsf{P}^{\mu}_{\nu}\left(x\right)\mathsf{Q}^{% \mu}_{\nu+1}\left(x\right)+\mathsf{P}^{\mu}_{\nu+1}\left(x\right)\mathsf{Q}^{% \mu}_{\nu}\left(x\right))+2(\mu-\nu-1)^{2}\mathsf{P}^{\mu}_{\nu+1}\left(x% \right)\mathsf{Q}^{\mu}_{\nu+1}\left(x\right)\right),}}

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DLMF:14.17.E4

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