DLMF:18.30.E7 (Q6005)

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DLMF:18.30.E7
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    Statements

    Defining formula
    P n ⁡ ( x ; c ) = ∑ ℓ = 0 n c ℓ + c ⁢ P ℓ ⁡ ( x ) ⁢ P n - ℓ ⁡ ( x ) . Legendre-spherical-polynomial-P 𝑛 𝑥 𝑐 superscript subscript ℓ 0 𝑛 𝑐 ℓ 𝑐 Legendre-spherical-polynomial ℓ 𝑥 Legendre-spherical-polynomial 𝑛 ℓ 𝑥 {\displaystyle{\displaystyle P_{n}\left(x;c\right)=\sum_{\ell=0}^{n}\frac{c}{% \ell+c}P_{\ell}\left(x\right)P_{n-\ell}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.30.E7
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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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    associated Legendre polynomial
    Defining formula
    P n ⁡ ( x ; c ) Legendre-spherical-polynomial-P 𝑛 𝑥 𝑐 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x};\NVar{c}\right)}}
    xml-id
    C18.S30.E6.m2aadec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1adec
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