DLMF:14.9.E3 (Q4793): Difference between revisions

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DLMF:14.9.E3
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    Statements

    Defining formula
    𝖯 ν - m ⁡ ( x ) = ( - 1 ) m ⁢ Γ ⁡ ( ν - m + 1 ) Γ ⁡ ( ν + m + 1 ) ⁢ 𝖯 ν m ⁡ ( x ) , Ferrers-Legendre-P-first-kind 𝑚 𝜈 𝑥 superscript 1 𝑚 Euler-Gamma 𝜈 𝑚 1 Euler-Gamma 𝜈 𝑚 1 Ferrers-Legendre-P-first-kind 𝑚 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{-m}_{\nu}\left(x\right)=(-1)^{m}\frac{% \Gamma\left(\nu-m+1\right)}{\Gamma\left(\nu+m+1\right)}\mathsf{P}^{m}_{\nu}% \left(x\right),}}
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    DLMF id
    DLMF:14.9.E3
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