DLMF:14.7.E1 (Q5448)

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DLMF:14.7.E1
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    Statements

    DLMF defining formula
    𝖯 n 0 ⁡ ( x ) = 𝖯 n ⁡ ( x ) = P n 0 ⁡ ( x ) = P n ⁡ ( x ) , Ferrers-Legendre-P-first-kind 0 𝑛 𝑥 shorthand-Ferrers-Legendre-P-first-kind 𝑛 𝑥 Legendre-P-first-kind 0 𝑛 𝑥 Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{0}_{n}\left(x\right)=\mathsf{P}_{n}% \left(x\right)=P^{0}_{n}\left(x\right)=P_{n}\left(x\right),}}
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    constraint
    x ∈ ℝ 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}
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    Symbols used
    Ferrers function of the first kind
    DLMF 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.m2adec
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    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
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    Legendre polynomial
    DLMF defining formula
    P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r10.m2adec
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    Q10758
    DLMF defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
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    Q10786
    DLMF defining formula
    ℝ {\displaystyle{\displaystyle\mathbb{R}}}
    xml-id
    introduction.Sx4.p2.t1.r14.m2adec
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    Q11566
    DLMF defining formula
    𝖯 ν ⁡ ( x ) = 𝖯 ν 0 ⁡ ( x ) shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑥 Ferrers-Legendre-P-first-kind 0 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{P}^{0}_{\nu}\left(x\right)}}
    xml-id
    C14.S2.SS2.p2.m2adec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1dec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1dec
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    Identifiers

     
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