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DLMF:14.10.E7 - MaRDI portal

DLMF:14.10.E7 (Q5513)

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DLMF:14.10.E7
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    Statements

    DLMF defining formula
    ( x 2 - 1 ) 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 superscript 𝑥 2 1 1 2 Legendre-P-first-kind 𝜇 1 𝜈 𝑥 𝜈 𝜇 1 Legendre-P-first-kind 𝜇 𝜈 1 𝑥 𝜈 𝜇 1 𝑥 Legendre-P-first-kind 𝜇 𝜈 𝑥 0 {\displaystyle{\displaystyle{\left(x^{2}-1\right)^{1/2}P^{\mu+1}_{\nu}\left(x% \right)-(\nu-\mu+1)P^{\mu}_{\nu+1}\left(x\right)}+(\nu+\mu+1)xP^{\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.m1aadec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1fdec
    0 references
    general order
    DLMF defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1fdec
    0 references
    general degree
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1fdec
    0 references

    Identifiers

     
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