DLMF:14.7.E13 (Q4765)

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DLMF:14.7.E13
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    Statements

    Defining formula
    P n ⁡ ( x ) = 1 2 n ⁢ n ! ⁢ d n d x n ⁡ ( x 2 - 1 ) n , Legendre-spherical-polynomial 𝑛 𝑥 1 superscript 2 𝑛 𝑛 derivative 𝑥 𝑛 superscript superscript 𝑥 2 1 𝑛 {\displaystyle{\displaystyle P_{n}\left(x\right)=\frac{1}{2^{n}n!}\frac{{% \mathrm{d}}^{n}}{{\mathrm{d}x}^{n}}\left(x^{2}-1\right)^{n},}}
    0 references
    DLMF id
    DLMF:14.7.E13
    0 references
    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.m2aedec
    0 references
     
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