DLMF:18.12.E4 (Q5646)

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Language	Label	Description	Also known as
English	DLMF:18.12.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle(1-2xz+z^{2})^{-\lambda}=\sum_{n=0}^{\infty}C^{(% \lambda)}_{n}\left(x\right)z^{n}=\sum_{n=0}^{\infty}\frac{{\left(2\lambda% \right)_{n}}}{{\left(\lambda+\tfrac{1}{2}\right)_{n}}}P^{(\lambda-\frac{1}{2},% \lambda-\frac{1}{2})}_{n}\left(x\right)z^{n},}}

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DLMF:18.12.E4

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{\displaystyle{\displaystyle|z|<1}}

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Defining formula

{\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}

C18.S3.T1.t1.r2.m2acdec

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Defining formula

{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

C5.S2.SS3.m1aadec

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Defining formula

{\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}

C18.S3.T1.t1.r3.m2adec

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Defining formula

{\displaystyle{\displaystyle z}}

C18.S1.XMD2.m1cdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1cdec

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