DLMF:14.7.E16 (Q4768)

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DLMF:14.7.E16
No description defined

    Statements

    Defining formula
    𝖯 n m ⁡ ( x ) = P n m ⁡ ( x ) = 0 , Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 Legendre-P-first-kind 𝑚 𝑛 𝑥 0 {\displaystyle{\displaystyle\mathsf{P}^{m}_{n}\left(x\right)=P^{m}_{n}\left(x% \right)=0,}}
    0 references
    DLMF id
    DLMF:14.7.E16
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    constraint
    m > n 𝑚 𝑛 {\displaystyle{\displaystyle m>n}}
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    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.m2acdec
    0 references
    Q11481
    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.m1addec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1odec
    0 references
    Q11593
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1gdec
    0 references
    Q11602
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1mdec
    0 references
     
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