DLMF:14.7.E8 (Q4760): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
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.m2aadec

Revision as of 01:28, 2 January 2020

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DLMF:14.7.E8
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    Statements

    𝖯 n m ( x ) = ( - 1 ) m ( 1 - x 2 ) m / 2 d m d x m 𝖯 n ( x ) , Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 superscript 1 𝑚 superscript 1 superscript 𝑥 2 𝑚 2 derivative 𝑥 𝑚 shorthand-Ferrers-Legendre-P-first-kind 𝑛 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{m}_{n}\left(x\right)=(-1)^{m}\left(1-x% ^{2}\right)^{m/2}\frac{{\mathrm{d}}^{m}}{{\mathrm{d}x}^{m}}\mathsf{P}_{n}\left% (x\right),}}
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    DLMF:14.7.E8
    0 references
    𝖯 ν μ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    C14.S3.E1.m2aadec
    0 references