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DLMF:14.10.E6 - MaRDI portal

DLMF:14.10.E6 (Q5512)

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DLMF:14.10.E6
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    Statements

    DLMF defining formula
    P ν μ + 2 ⁡ ( x ) + 2 ⁢ ( μ + 1 ) ⁢ x ⁢ ( x 2 - 1 ) - 1 / 2 ⁢ P ν μ + 1 ⁡ ( x ) - ( ν - μ ) ⁢ ( ν + μ + 1 ) ⁢ P ν μ ⁡ ( x ) = 0 , Legendre-P-first-kind 𝜇 2 𝜈 𝑥 2 𝜇 1 𝑥 superscript superscript 𝑥 2 1 1 2 Legendre-P-first-kind 𝜇 1 𝜈 𝑥 𝜈 𝜇 𝜈 𝜇 1 Legendre-P-first-kind 𝜇 𝜈 𝑥 0 {\displaystyle{\displaystyle{P^{\mu+2}_{\nu}\left(x\right)+2(\mu+1)x\left(x^{2% }-1\right)^{-1/2}P^{\mu+1}_{\nu}\left(x\right)}-(\nu-\mu)(\nu+\mu+1)P^{\mu}_{% \nu}\left(x\right)=0,}}
    0 references
    Symbols used
    associated Legendre function of the first kind
    DLMF defining formula
    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.m1adec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1edec
    0 references
    general order
    DLMF defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1edec
    0 references
    general degree
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1edec
    0 references
     
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