DLMF:14.17.E3 (Q4884)

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Language	Label	Description	Also known as
English	DLMF:14.17.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int x\mathsf{P}^{\mu}_{\nu}\left(x\right)\mathsf{% Q}^{\mu}_{\nu}\left(x\right)\mathrm{d}x=\frac{1}{2\nu(\nu+1)}\left((\mu^{2}-(% \nu+1)(\nu+x^{2}))\mathsf{P}^{\mu}_{\nu}\left(x\right)\mathsf{Q}^{\mu}_{\nu}% \left(x\right)+(\nu+1)(\nu-\mu+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))-(\nu-\mu+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.E3

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{\displaystyle{\displaystyle\nu\neq 0,-1}}

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Ferrers function of the first kind

Defining formula

{\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C14.S3.E1.m2abdec

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Ferrers function of the second kind

Defining formula

{\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C14.S3.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1abdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abdec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1bdec

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