DLMF:18.10.E2 (Q5626)

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DLMF:18.10.E2
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    Defining formula
    P n ⁡ ( cos ⁡ θ ) = 2 1 2 π ⁢ ∫ 0 θ cos ⁡ ( ( n + 1 2 ) ⁢ ϕ ) ( cos ⁡ ϕ - cos ⁡ θ ) 1 2 ⁢ d ϕ , Legendre-spherical-polynomial 𝑛 𝜃 superscript 2 1 2 𝜋 superscript subscript 0 𝜃 𝑛 1 2 italic-ϕ superscript italic-ϕ 𝜃 1 2 italic-ϕ {\displaystyle{\displaystyle P_{n}\left(\cos\theta\right)=\frac{2^{\frac{1}{2}% }}{\pi}\int_{0}^{\theta}\frac{\cos\left((n+\tfrac{1}{2})\phi\right)}{(\cos\phi% -\cos\theta)^{\frac{1}{2}}}\mathrm{d}\phi,}}
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    DLMF id
    DLMF:18.10.E2
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