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

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.m2aedec

Revision as of 13:44, 2 January 2020

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DLMF:14.30.E8
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    Statements

    Defining formula
    ∫ 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}}.}}
    0 references
    DLMF id
    DLMF:14.30.E8
    0 references
    Symbols used
    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
     
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