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DLMF:14.7.E4 - MaRDI portal

DLMF:14.7.E4 (Q5451)

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DLMF:14.7.E4
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    Statements

    DLMF defining formula
    W n - 1 ⁢ ( x ) = ∑ k = 1 n 1 k ⁢ P k - 1 ⁡ ( x ) ⁢ P n - k ⁡ ( x ) . subscript 𝑊 𝑛 1 𝑥 superscript subscript 𝑘 1 𝑛 1 𝑘 Legendre-spherical-polynomial 𝑘 1 𝑥 Legendre-spherical-polynomial 𝑛 𝑘 𝑥 {\displaystyle{\displaystyle W_{n-1}(x)=\sum_{k=1}^{n}\frac{1}{k}P_{k-1}\left(% x\right)P_{n-k}\left(x\right).}}
    0 references
    Symbols used
    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.m2abdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1cdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1cdec
    0 references
    quantity
    DLMF defining formula
    W n - 1 ⁢ ( x ) subscript 𝑊 𝑛 1 𝑥 {\displaystyle{\displaystyle W_{n-1}(x)}}
    xml-id
    C14.S7.XMD1.m1bdec
    0 references

    Identifiers

     
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