DLMF:14.3.E4 (Q4693)

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DLMF:14.3.E4
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    Defining formula
    𝖯 ν m ⁡ ( x ) = ( - 1 ) m ⁢ Γ ⁡ ( ν + m + 1 ) 2 m ⁢ Γ ⁡ ( ν - m + 1 ) ⁢ ( 1 - x 2 ) m / 2 ⁢ 𝐅 ⁡ ( ν + m + 1 , m - ν ; m + 1 ; 1 2 - 1 2 ⁢ x ) ; Ferrers-Legendre-P-first-kind 𝑚 𝜈 𝑥 superscript 1 𝑚 Euler-Gamma 𝜈 𝑚 1 superscript 2 𝑚 Euler-Gamma 𝜈 𝑚 1 superscript 1 superscript 𝑥 2 𝑚 2 scaled-hypergeometric-bold-F 𝜈 𝑚 1 𝑚 𝜈 𝑚 1 1 2 1 2 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{m}_{\nu}\left(x\right)=(-1)^{m}\frac{% \Gamma\left(\nu+m+1\right)}{2^{m}\Gamma\left(\nu-m+1\right)}\left(1-x^{2}% \right)^{m/2}\mathbf{F}\left(\nu+m+1,m-\nu;m+1;\tfrac{1}{2}-\tfrac{1}{2}x% \right);}}
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    DLMF id
    DLMF:14.3.E4
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