DLMF:1.17.E25 (Q684): Difference between revisions

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

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2adec

Revision as of 16:46, 1 January 2020

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DLMF:1.17.E25
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    Statements

    Defining formula
    δ ⁡ ( cos ⁡ θ 1 - cos ⁡ θ 2 ) ⁢ δ ⁡ ( ϕ 1 - ϕ 2 ) = ∑ ℓ = 0 ∞ ∑ m = - ℓ ℓ Y ℓ , m ⁡ ( θ 1 , ϕ 1 ) ⁢ Y ℓ , m ⁡ ( θ 2 , ϕ 2 ) ¯ . Dirac-delta subscript 𝜃 1 subscript 𝜃 2 Dirac-delta subscript italic-ϕ 1 subscript italic-ϕ 2 superscript subscript ℓ 0 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\delta\left(\cos\theta_{1}-\cos\theta_{2}\right)% \delta\left(\phi_{1}-\phi_{2}\right)=\sum_{\ell=0}^{\infty}\sum_{m=-\ell}^{% \ell}Y_{{\ell},{m}}\left(\theta_{1},\phi_{1}\right)\overline{Y_{{\ell},{m}}% \left(\theta_{2},\phi_{2}\right)}.}}
    0 references
    DLMF id
    DLMF:1.17.E25
    0 references
    Symbols used
    Q10915
    Defining formula
    δ ⁡ ( x - a ) Dirac-delta 𝑥 𝑎 {\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}
    xml-id
    C1.S17.SS1.p1.m2aldec
    0 references
    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2adec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
     
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