DLMF:18.14.E10 (Q5673)

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DLMF:18.14.E10
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    Statements

    Defining formula
    ( P n ⁡ ( x ) ) 2 ≥ P n - 1 ⁡ ( x ) ⁢ P n + 1 ⁡ ( x ) , superscript Legendre-spherical-polynomial 𝑛 𝑥 2 Legendre-spherical-polynomial 𝑛 1 𝑥 Legendre-spherical-polynomial 𝑛 1 𝑥 {\displaystyle{\displaystyle(P_{n}\left(x\right))^{2}\geq P_{n-1}\left(x\right% )P_{n+1}\left(x\right),}}
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    DLMF id
    DLMF:18.14.E10
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    constraint
    - 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}}
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    Symbols used
    Q10920
    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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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1gdec
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    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1idec
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