DLMF:14.8.E14 (Q4788)

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DLMF:14.8.E14
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    Defining formula
    P - 1 / 2 μ ⁡ ( x ) ∼ 1 Γ ⁡ ( 1 2 - μ ) ⁢ ( 2 π ⁢ x ) 1 / 2 ⁢ ln ⁡ x , asymptotically-equals Legendre-P-first-kind 𝜇 1 2 𝑥 1 Euler-Gamma 1 2 𝜇 superscript 2 𝜋 𝑥 1 2 𝑥 {\displaystyle{\displaystyle P^{\mu}_{-1/2}\left(x\right)\sim\frac{1}{\Gamma% \left(\frac{1}{2}-\mu\right)}\left(\frac{2}{\pi x}\right)^{1/2}\ln x,}}
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    DLMF id
    DLMF:14.8.E14
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