DLMF:14.3.E1 (Q4690)

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DLMF:14.3.E1
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    𝖯 ν μ ⁡ ( x ) = ( 1 + x 1 - x ) μ / 2 ⁢ 𝐅 ⁡ ( ν + 1 , - ν ; 1 - μ ; 1 2 - 1 2 ⁢ x ) . Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 superscript 1 𝑥 1 𝑥 𝜇 2 scaled-hypergeometric-bold-F 𝜈 1 𝜈 1 𝜇 1 2 1 2 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu}\left(x\right)=\left(\frac{1% +x}{1-x}\right)^{\mu/2}\mathbf{F}\left(\nu+1,-\nu;1-\mu;\tfrac{1}{2}-\tfrac{1}% {2}x\right).}}
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    DLMF:14.3.E1
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