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

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Property / Symbols used
 
Property / Symbols used: complex conjugate / rank
 
Normal rank
Property / Symbols used: complex conjugate / qualifier
 
test:

z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}

\conj{\NVar{z}}
Property / Symbols used: complex conjugate / qualifier
 
xml-id: C1.S9.E11.m2abdec

Revision as of 12:44, 2 January 2020

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DLMF:14.30.E9
No description defined

    Statements

    test
    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).}}
    0 references
    DLMF id
    DLMF:14.30.E9
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    complex conjugate
    test
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2abdec
    0 references
     
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