DLMF:14.10.E2 (Q4811): Difference between revisions

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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.m2aadec

Revision as of 00:38, 2 January 2020

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DLMF:14.10.E2
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    Statements

    test
    ( 1 - x 2 ) 1 / 2 ⁢ 𝖯 ν μ + 1 ⁡ ( x ) - ( ν - μ + 1 ) ⁢ 𝖯 ν + 1 μ ⁡ ( x ) + ( ν + μ + 1 ) ⁢ x ⁢ 𝖯 ν μ ⁡ ( x ) = 0 , superscript 1 superscript 𝑥 2 1 2 Ferrers-Legendre-P-first-kind 𝜇 1 𝜈 𝑥 𝜈 𝜇 1 Ferrers-Legendre-P-first-kind 𝜇 𝜈 1 𝑥 𝜈 𝜇 1 𝑥 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 0 {\displaystyle{\displaystyle{\left(1-x^{2}\right)^{1/2}\mathsf{P}^{\mu+1}_{\nu% }\left(x\right)-(\nu-\mu+1)\mathsf{P}^{\mu}_{\nu+1}\left(x\right)}+(\nu+\mu+1)% x\mathsf{P}^{\mu}_{\nu}\left(x\right)=0,}}
    0 references
    DLMF id
    DLMF:14.10.E2
    0 references
    Symbols used
    Ferrers function of the first kind
    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)}}
    xml-id
    C14.S3.E1.m2aadec
    0 references
     
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