DLMF:14.6.E6 (Q4748): 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 01:27, 2 January 2020

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DLMF:14.6.E6
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    Statements

    𝖯 ν - m ( x ) = ( 1 - x 2 ) - m / 2 x 1 x 1 P ν ( x ) ( d x ) m . Ferrers-Legendre-P-first-kind 𝑚 𝜈 𝑥 superscript 1 superscript 𝑥 2 𝑚 2 superscript subscript 𝑥 1 superscript subscript 𝑥 1 shorthand-Legendre-P-first-kind 𝜈 𝑥 superscript 𝑥 𝑚 {\displaystyle{\displaystyle\mathsf{P}^{-m}_{\nu}\left(x\right)=\left(1-x^{2}% \right)^{-m/2}\int_{x}^{1}\!\dots\!\int_{x}^{1}P_{\nu}\left(x\right)\left(\!% \mathrm{d}x\right)^{m}.}}
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    DLMF:14.6.E6
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    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