DLMF:14.30.E9 (Q4971): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
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Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2afdec

Revision as of 12:44, 2 January 2020

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DLMF:14.30.E9
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    𝖯 l ( cos θ 1 cos θ 2 + sin θ 1 sin θ 2 cos ( ϕ 1 - ϕ 2 ) ) = 4 π 2 l + 1 m = - l l Y l , m ( θ 1 , ϕ 1 ) ¯ Y l , m ( θ 2 , ϕ 2 ) . shorthand-Ferrers-Legendre-P-first-kind 𝑙 subscript 𝜃 1 subscript 𝜃 2 subscript 𝜃 1 subscript 𝜃 2 subscript italic-ϕ 1 subscript italic-ϕ 2 4 𝜋 2 𝑙 1 superscript subscript 𝑚 𝑙 𝑙 spherical-harmonic-Y 𝑙 𝑚 subscript 𝜃 1 subscript italic-ϕ 1 spherical-harmonic-Y 𝑙 𝑚 subscript 𝜃 2 subscript italic-ϕ 2 {\displaystyle{\displaystyle\mathsf{P}_{l}\left(\cos\theta_{1}\cos\theta_{2}+% \sin\theta_{1}\sin\theta_{2}\cos\left(\phi_{1}-\phi_{2}\right)\right)=\frac{4% \pi}{2l+1}\sum_{m=-l}^{l}\overline{Y_{{l},{m}}\left(\theta_{1},\phi_{1}\right)% }Y_{{l},{m}}\left(\theta_{2},\phi_{2}\right).}}
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2afdec
    0 references