DLMF:14.30.E1 (Q4963): Difference between revisions

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‎Changed an Item: Wikidata Toolkit example test statement addition
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Ferrers function of the first kind / rank
 
Normal rank
Property / Symbols used: Ferrers function of the first kind / qualifier
 
Defining formula:

𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

\FerrersP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Ferrers function of the first kind / qualifier
 
xml-id: C14.S3.E1.m2adec

Revision as of 13:42, 2 January 2020

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DLMF:14.30.E1
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    Statements

    Defining formula
    Y l , m ⁡ ( θ , ϕ ) = ( ( l - m ) ! ⁢ ( 2 ⁢ l + 1 ) 4 ⁢ π ⁢ ( l + m ) ! ) 1 / 2 ⁢ e i ⁢ m ⁢ ϕ ⁢ 𝖯 l m ⁡ ( cos ⁡ θ ) , spherical-harmonic-Y 𝑙 𝑚 𝜃 italic-ϕ superscript 𝑙 𝑚 2 𝑙 1 4 𝜋 𝑙 𝑚 1 2 superscript 𝑒 𝑖 𝑚 italic-ϕ Ferrers-Legendre-P-first-kind 𝑚 𝑙 𝜃 {\displaystyle{\displaystyle Y_{{l},{m}}\left(\theta,\phi\right)=\left(\frac{(% l-m)!(2l+1)}{4\pi(l+m)!}\right)^{1/2}e^{im\phi}\mathsf{P}^{m}_{l}\left(\cos% \theta\right),}}
    0 references
    DLMF id
    DLMF:14.30.E1
    0 references
    Symbols used
    Ferrers function of the first kind
    Defining formula
    𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E1.m2adec
    0 references
     
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