DLMF:14.10.E3 (Q4812)

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DLMF:14.10.E3
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    Statements

    Defining formula
    ( ν - μ + 2 ) ⁢ 𝖯 ν + 2 μ ⁡ ( x ) - ( 2 ⁢ ν + 3 ) ⁢ x ⁢ 𝖯 ν + 1 μ ⁡ ( x ) + ( ν + μ + 1 ) ⁢ 𝖯 ν μ ⁡ ( x ) = 0 , 𝜈 𝜇 2 Ferrers-Legendre-P-first-kind 𝜇 𝜈 2 𝑥 2 𝜈 3 𝑥 Ferrers-Legendre-P-first-kind 𝜇 𝜈 1 𝑥 𝜈 𝜇 1 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 0 {\displaystyle{\displaystyle{(\nu-\mu+2)\mathsf{P}^{\mu}_{\nu+2}\left(x\right)% -(2\nu+3)x\mathsf{P}^{\mu}_{\nu+1}\left(x\right)}+(\nu+\mu+1)\mathsf{P}^{\mu}_% {\nu}\left(x\right)=0,}}
    0 references
    DLMF id
    DLMF:14.10.E3
    0 references
    Symbols used
    Ferrers function of the first kind
    Defining formula
    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.m2abdec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1bdec
    0 references
     
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