DLMF:14.18.E8 (Q4909)

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DLMF:14.18.E8
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    test
    𝖯 ν ⁡ ( - x ) = sin ⁡ ( ν ⁢ π ) π ⁢ ∑ n = 0 ∞ 2 ⁢ n + 1 ( ν - n ) ⁢ ( ν + n + 1 ) ⁢ 𝖯 n ⁡ ( x ) , shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑥 𝜈 𝜋 𝜋 superscript subscript 𝑛 0 2 𝑛 1 𝜈 𝑛 𝜈 𝑛 1 shorthand-Ferrers-Legendre-P-first-kind 𝑛 𝑥 {\displaystyle{\displaystyle\mathsf{P}_{\nu}\left(-x\right)=\frac{\sin\left(% \nu\pi\right)}{\pi}\sum_{n=0}^{\infty}\frac{2n+1}{(\nu-n)(\nu+n+1)}\mathsf{P}_% {n}\left(x\right),}}
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    DLMF:14.18.E8
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