DLMF:14.10.E5 (Q4814)

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DLMF:14.10.E5
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    Defining formula
    ( 1 - x 2 ) ⁢ d 𝖯 ν μ ⁡ ( x ) d x = ( ν + μ ) ⁢ 𝖯 ν - 1 μ ⁡ ( x ) - ν ⁢ x ⁢ 𝖯 ν μ ⁡ ( x ) . 1 superscript 𝑥 2 derivative Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝑥 𝜈 𝜇 Ferrers-Legendre-P-first-kind 𝜇 𝜈 1 𝑥 𝜈 𝑥 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\left(1-x^{2}\right)\frac{\mathrm{d}\mathsf{P}^{% \mu}_{\nu}\left(x\right)}{\mathrm{d}x}=(\nu+\mu)\mathsf{P}^{\mu}_{\nu-1}\left(% x\right)-\nu x\mathsf{P}^{\mu}_{\nu}\left(x\right).}}
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    DLMF id
    DLMF:14.10.E5
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