DLMF:18.17.E6 (Q5747)

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DLMF:18.17.E6
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    P n ⁡ ( cos ⁡ θ 1 ) ⁢ P n ⁡ ( cos ⁡ θ 2 ) = 1 π ⁢ ∫ 0 π P n ⁡ ( cos ⁡ θ 1 ⁢ cos ⁡ θ 2 + sin ⁡ θ 1 ⁢ sin ⁡ θ 2 ⁢ cos ⁡ ϕ ) ⁢ d ϕ . Legendre-spherical-polynomial 𝑛 subscript 𝜃 1 Legendre-spherical-polynomial 𝑛 subscript 𝜃 2 1 𝜋 superscript subscript 0 𝜋 Legendre-spherical-polynomial 𝑛 subscript 𝜃 1 subscript 𝜃 2 subscript 𝜃 1 subscript 𝜃 2 italic-ϕ italic-ϕ {\displaystyle{\displaystyle P_{n}\left(\cos\theta_{1}\right)P_{n}\left(\cos% \theta_{2}\right)=\frac{1}{\pi}\int_{0}^{\pi}P_{n}\left(\cos\theta_{1}\cos% \theta_{2}+\sin\theta_{1}\sin\theta_{2}\cos\phi\right)\mathrm{d}\phi.}}
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    DLMF:18.17.E6
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