DLMF:14.30.E8 (Q4970): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11642 / rank
 
Normal rank
Property / Symbols used: Q11642 / qualifier
 
Defining formula:

l 𝑙 {\displaystyle{\displaystyle l}}

l
Property / Symbols used: Q11642 / qualifier
 
xml-id: C14.S30.XMD2.m1gdec

Latest revision as of 13:44, 2 January 2020

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DLMF:14.30.E8
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    Statements

    0 2 π 0 π Y l 1 , m 1 ( θ , ϕ ) ¯ Y l 2 , m 2 ( θ , ϕ ) sin θ d θ d ϕ = δ l 1 , l 2 δ m 1 , m 2 . superscript subscript 0 2 𝜋 superscript subscript 0 𝜋 spherical-harmonic-Y subscript 𝑙 1 subscript 𝑚 1 𝜃 italic-ϕ spherical-harmonic-Y subscript 𝑙 2 subscript 𝑚 2 𝜃 italic-ϕ 𝜃 𝜃 italic-ϕ Kronecker subscript 𝑙 1 subscript 𝑙 2 Kronecker subscript 𝑚 1 subscript 𝑚 2 {\displaystyle{\displaystyle\int_{0}^{2\pi}\!\!\int_{0}^{\pi}\overline{Y_{{l_{% 1}},{m_{1}}}\left(\theta,\phi\right)}Y_{{l_{2}},{m_{2}}}\left(\theta,\phi% \right)\sin\theta\mathrm{d}\theta\mathrm{d}\phi=\delta_{l_{1},l_{2}}\delta_{m_% {1},m_{2}}.}}
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    DLMF:14.30.E8
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    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    introduction.Sx4.p1.t1.r4.m5adec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aedec
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    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    C1.S9.E11.m2aadec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1adec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3adec
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    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2abdec
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    Y l , m ( θ , ϕ ) spherical-harmonic-Y 𝑙 𝑚 𝜃 italic-ϕ {\displaystyle{\displaystyle Y_{{\NVar{l}},{\NVar{m}}}\left(\NVar{\theta},% \NVar{\phi}\right)}}
    C14.S30.E1.m2afdec
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    m 𝑚 {\displaystyle{\displaystyle m}}
    C14.S30.XMD1.m1gdec
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    l 𝑙 {\displaystyle{\displaystyle l}}
    C14.S30.XMD2.m1gdec
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