DLMF:14.10.E2 (Q4811)

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DLMF:14.10.E2
No description defined

    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
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    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1adec
    0 references
    Q11591
    test
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1adec
    0 references
    Q11590
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1adec
    0 references
     
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