DLMF:14.30.E7 (Q4969): Difference between revisions

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

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)}}

\sphharmonicY{\NVar{l}}{\NVar{m}}@{\NVar{\theta}}{\NVar{\phi}}
Property / Symbols used: spherical harmonic / qualifier
 
xml-id: C14.S30.E1.m2aedec

Revision as of 13:44, 2 January 2020

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DLMF:14.30.E7
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    Statements

    Defining formula
    Y l , m ⁡ ( π - θ , ϕ + π ) = ( - 1 ) l ⁢ Y l , m ⁡ ( θ , ϕ ) . spherical-harmonic-Y 𝑙 𝑚 𝜋 𝜃 italic-ϕ 𝜋 superscript 1 𝑙 spherical-harmonic-Y 𝑙 𝑚 𝜃 italic-ϕ {\displaystyle{\displaystyle Y_{{l},{m}}\left(\pi-\theta,\phi+\pi\right)=(-1)^% {l}Y_{{l},{m}}\left(\theta,\phi\right).}}
    0 references
    DLMF id
    DLMF:14.30.E7
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    spherical harmonic
    Defining formula
    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)}}
    xml-id
    C14.S30.E1.m2aedec
    0 references
     
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