DLMF:14.7.E11 (Q4763): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10920 / rank
 
Normal rank
Property / Symbols used: Q10920 / qualifier
 
test:

P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}

\LegendrepolyP{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q10920 / qualifier
 
xml-id: C18.S3.T1.t1.r10.m2addec

Revision as of 00:29, 2 January 2020

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DLMF:14.7.E11
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    Statements

    test
    P n m ⁡ ( x ) = ( x 2 - 1 ) m / 2 ⁢ d m d x m ⁡ P n ⁡ ( x ) , Legendre-P-first-kind 𝑚 𝑛 𝑥 superscript superscript 𝑥 2 1 𝑚 2 derivative 𝑥 𝑚 Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P^{m}_{n}\left(x\right)=\left(x^{2}-1\right)^{m/2% }\frac{{\mathrm{d}}^{m}}{{\mathrm{d}x}^{m}}P_{n}\left(x\right),}}
    0 references
    DLMF id
    DLMF:14.7.E11
    0 references
    Symbols used
    Q11481
    test
    P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m1aadec
    0 references
    Q10920
    test
    P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r10.m2addec
    0 references
     
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