DLMF:14.30.E3 (Q4965): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aadec

Revision as of 13:43, 2 January 2020

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DLMF:14.30.E3
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    Statements

    Y l , m ( θ , ϕ ) = ( - 1 ) l + m 2 l l ! ( ( l - m ) ! ( 2 l + 1 ) 4 π ( l + m ) ! ) 1 / 2 e i m ϕ ( sin θ ) m ( d d ( cos θ ) ) l + m ( sin θ ) 2 l . spherical-harmonic-Y 𝑙 𝑚 𝜃 italic-ϕ superscript 1 𝑙 𝑚 superscript 2 𝑙 𝑙 superscript 𝑙 𝑚 2 𝑙 1 4 𝜋 𝑙 𝑚 1 2 superscript 𝑒 𝑖 𝑚 italic-ϕ superscript 𝜃 𝑚 superscript derivative 𝜃 𝑙 𝑚 superscript 𝜃 2 𝑙 {\displaystyle{\displaystyle Y_{{l},{m}}\left(\theta,\phi\right)=\frac{(-1)^{l% +m}}{2^{l}l!}\left(\frac{(l-m)!(2l+1)}{4\pi(l+m)!}\right)^{1/2}e^{im\phi}\left% (\sin\theta\right)^{m}\*\left(\frac{\mathrm{d}}{\mathrm{d}(\cos\theta)}\right)% ^{l+m}\left(\sin\theta\right)^{2l}.}}
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    DLMF:14.30.E3
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
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    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2abdec
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    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2adec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aadec
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    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5aadec
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