DLMF:14.6.E1 (Q4743): Difference between revisions

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imported>Admin
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
 
test:

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 00:26, 2 January 2020

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DLMF:14.6.E1
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    Statements

    𝖯 ν m ( x ) = ( - 1 ) m ( 1 - x 2 ) m / 2 d m 𝖯 ν ( x ) d x m , Ferrers-Legendre-P-first-kind 𝑚 𝜈 𝑥 superscript 1 𝑚 superscript 1 superscript 𝑥 2 𝑚 2 derivative shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑥 𝑥 𝑚 {\displaystyle{\displaystyle\mathsf{P}^{m}_{\nu}\left(x\right)=(-1)^{m}\left(1% -x^{2}\right)^{m/2}\frac{{\mathrm{d}}^{m}\mathsf{P}_{\nu}\left(x\right)}{{% \mathrm{d}x}^{m}},}}
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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.m2adec
    0 references