DLMF:14.18.E2 (Q4903)

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DLMF:14.18.E2
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    𝖯 n ( cos θ 1 cos θ 2 + sin θ 1 sin θ 2 cos ϕ ) = m = - n n ( - 1 ) m 𝖯 n - m ( cos θ 1 ) 𝖯 n m ( cos θ 2 ) cos ( m ϕ ) . shorthand-Ferrers-Legendre-P-first-kind 𝑛 subscript 𝜃 1 subscript 𝜃 2 subscript 𝜃 1 subscript 𝜃 2 italic-ϕ superscript subscript 𝑚 𝑛 𝑛 superscript 1 𝑚 Ferrers-Legendre-P-first-kind 𝑚 𝑛 subscript 𝜃 1 Ferrers-Legendre-P-first-kind 𝑚 𝑛 subscript 𝜃 2 𝑚 italic-ϕ {\displaystyle{\displaystyle\mathsf{P}_{n}\left(\cos\theta_{1}\cos\theta_{2}+% \sin\theta_{1}\sin\theta_{2}\cos\phi\right)=\sum_{m=-n}^{n}(-1)^{m}\mathsf{P}^% {-m}_{n}\left(\cos\theta_{1}\right)\mathsf{P}^{m}_{n}\left(\cos\theta_{2}% \right)\cos\left(m\phi\right).}}
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    DLMF:14.18.E2
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    𝖯 ν μ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    C14.S3.E1.m2aadec
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