DLMF:18.11.E1 (Q5635): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:18.11.E1	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathsf{P}^{m}_{n}\left(x\right)={\left(\tfrac{1}{% 2}\right)_{m}}(-2)^{m}(1-x^{2})^{\frac{1}{2}m}C^{(m+\frac{1}{2})}_{n-m}\left(x% \right)={\left(n+1\right)_{m}}(-2)^{-m}(1-x^{2})^{\frac{1}{2}m}P^{(m,m)}_{n-m}% \left(x\right),}}

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DLMF:18.11.E1

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{\displaystyle{\displaystyle 0\leq m\leq n}}

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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.m2adec

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Defining formula

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

C18.S3.T1.t1.r2.m2adec

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Defining formula

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

C5.S2.SS3.m1adec

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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 m}}

C18.S1.XMD5.m1dec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1dec

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