DLMF:18.17.E7 (Q5748)

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Language	Label	Description	Also known as
English	DLMF:18.17.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\left(P_{n}\left(x\right)\right)^{2}+4\pi^{-2}% \left(\mathsf{Q}_{n}\left(x\right)\right)^{2}=4\pi^{-2}\*\int_{1}^{\infty}Q_{n% }\left(x^{2}+(1-x^{2})t\right)(t^{2}-1)^{-\frac{1}{2}}\mathrm{d}t,}}

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DLMF:18.17.E7

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{\displaystyle{\displaystyle-1<x<1}}

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Defining formula

{\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}

C18.S3.T1.t1.r10.m2aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2abdec

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Defining formula

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

C1.S4.SS4.m1afdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3afdec

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Defining formula

{\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{Q}^{0}_{\nu}\left(x\right)}}

C14.S2.SS2.p2.m4adec

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Defining formula

{\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}% \left(z\right)}}

C14.S2.SS2.p2.m5adec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1fdec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1ddec

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