DLMF:14.13.E1 (Q4837)

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DLMF:14.13.E1
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    Statements

    test
    𝖯 ν μ ⁡ ( cos ⁡ θ ) = 2 μ + 1 ⁢ ( sin ⁡ θ ) μ π 1 / 2 ⁢ ∑ k = 0 ∞ Γ ⁡ ( ν + μ + k + 1 ) Γ ⁡ ( ν + k + 3 2 ) ⁢ ( μ + 1 2 ) k k ! ⁢ sin ⁡ ( ( ν + μ + 2 ⁢ k + 1 ) ⁢ θ ) , Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝜃 superscript 2 𝜇 1 superscript 𝜃 𝜇 superscript 𝜋 1 2 superscript subscript 𝑘 0 Euler-Gamma 𝜈 𝜇 𝑘 1 Euler-Gamma 𝜈 𝑘 3 2 Pochhammer 𝜇 1 2 𝑘 𝑘 𝜈 𝜇 2 𝑘 1 𝜃 {\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu}\left(\cos\theta\right)=% \frac{2^{\mu+1}(\sin\theta)^{\mu}}{\pi^{1/2}}\*\sum_{k=0}^{\infty}\frac{\Gamma% \left(\nu+\mu+k+1\right)}{\Gamma\left(\nu+k+\frac{3}{2}\right)}\frac{{\left(% \mu+\frac{1}{2}\right)_{k}}}{k!}\*\sin\left((\nu+\mu+2k+1)\theta\right),}}
    0 references
    DLMF id
    DLMF:14.13.E1
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
     
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