DLMF:14.9.E2 (Q4792)

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DLMF:14.9.E2
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    Statements

    test
    2 ⁢ sin ⁡ ( μ ⁢ π ) π ⁢ Γ ⁡ ( ν - μ + 1 ) ⁢ 𝖰 ν - μ ⁡ ( x ) = 1 Γ ⁡ ( ν + μ + 1 ) ⁢ 𝖯 ν μ ⁡ ( x ) - cos ⁡ ( μ ⁢ π ) Γ ⁡ ( ν - μ + 1 ) ⁢ 𝖯 ν - μ ⁡ ( x ) , 2 𝜇 𝜋 𝜋 Euler-Gamma 𝜈 𝜇 1 Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 1 Euler-Gamma 𝜈 𝜇 1 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝜇 𝜋 Euler-Gamma 𝜈 𝜇 1 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\frac{2\sin\left(\mu\pi\right)}{\pi\Gamma\left(\nu% -\mu+1\right)}\mathsf{Q}^{-\mu}_{\nu}\left(x\right)=\frac{1}{\Gamma\left(\nu+% \mu+1\right)}\mathsf{P}^{\mu}_{\nu}\left(x\right)-\frac{\cos\left(\mu\pi\right% )}{\Gamma\left(\nu-\mu+1\right)}\mathsf{P}^{-\mu}_{\nu}\left(x\right),}}
    0 references
    DLMF id
    DLMF:14.9.E2
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
     
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