DLMF:14.7.E17 (Q4769)

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DLMF:14.7.E17
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    Statements

    Defining formula
    𝖯 n m ⁡ ( - x ) = ( - 1 ) n - m ⁢ 𝖯 n m ⁡ ( x ) , Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 superscript 1 𝑛 𝑚 Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{m}_{n}\left(-x\right)=(-1)^{n-m}% \mathsf{P}^{m}_{n}\left(x\right),}}
    0 references
    DLMF id
    DLMF:14.7.E17
    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.m2addec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1pdec
    0 references
     
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