DLMF:14.30.E6 (Q4968): 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.m2adec
Property / Symbols used
 
Property / Symbols used: spherical harmonic / rank
 
Normal rank
Property / Symbols used: spherical harmonic / qualifier
 
test:

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.m2addec
Property / Symbols used
 
Property / Symbols used: Q11641 / rank
 
Normal rank
Property / Symbols used: Q11641 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11641 / qualifier
 
xml-id: C14.S30.XMD1.m1edec
Property / Symbols used
 
Property / Symbols used: Q11642 / rank
 
Normal rank
Property / Symbols used: Q11642 / qualifier
 
test:

l 𝑙 {\displaystyle{\displaystyle l}}

l
Property / Symbols used: Q11642 / qualifier
 
xml-id: C14.S30.XMD2.m1edec

Latest revision as of 12:44, 2 January 2020

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DLMF:14.30.E6
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    Statements

    Y l , - m ( θ , ϕ ) = ( - 1 ) m Y l , m ( θ , ϕ ) ¯ . spherical-harmonic-Y 𝑙 𝑚 𝜃 italic-ϕ superscript 1 𝑚 spherical-harmonic-Y 𝑙 𝑚 𝜃 italic-ϕ {\displaystyle{\displaystyle Y_{{l},{-m}}\left(\theta,\phi\right)=(-1)^{m}% \overline{Y_{{l},{m}}\left(\theta,\phi\right)}.}}
    0 references
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    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    C1.S9.E11.m2adec
    0 references
    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.m2addec
    0 references
    m 𝑚 {\displaystyle{\displaystyle m}}
    C14.S30.XMD1.m1edec
    0 references
    l 𝑙 {\displaystyle{\displaystyle l}}
    C14.S30.XMD2.m1edec
    0 references